#incircle

[the-math-one]

Here's the image I'm using for my blog

[gayspock]

im off work for a weeknow properly. now fucking what.

[sillysymbol]

THE LGBT COMMUNITY HAS FORGIVEN THE MOJO CHESSMASTER

[daughterearth]

Reminder to me who feels super hopeless watching too much news and YouTube and shit which makes me internally sick:::: despite it all, despite all the scary painful, abusive, downright despiteful and horrifying shit that happens in the world::::: someone will always write stories about strange textures of grief and end it with love, someone will always call just to remind you that they think of you, some random person will buy flowers for their mother, some person on the planet will take care of their aging grandma, someone will always plant gorgeous yellow flowers in the yard, the lil kids would still wave, people would still pray before going to bed. Despite it all, love will exist, in words, actions, nature and souls. Always.

[loriparrish]

Please visit the community at LoriAndCompany.com to share your posts, events or privately submit a question, image or csv.

[6okuto]

NIA THE LUKE PEARCE MENTION IN THAT AWARD COVERED WITH LIPSTICK POST HAS ME FALLIG TO MY KNEES !!! LUKE 😭💗

PLEAAASEE VIE 😭😭 he wouldn't expect it he'd be standing up then his face would go 😯 when u grab his face and kiss him ☹️ he'd take 3 seconds to process it and be flustered while he's on stage but of course mention u like. couldn't have done it without my lovely ___! nd he blushes while he scratches his face and says a little joke abt the lipstick on his cheek 🙁 then when he gets back he relaxes and sighs as he closes his eyes and leans back into his seat... opens them when u say something & pulls u closer to whisper in ur ear about not forgetting the lipstick on his face and paying u back later when ur home WOAHHH WHO SAID THAT 😂

[icubuzz]

Dutch orchestra leader Andre Rieu is on tour. Listen and be blessed.

[v3nomly]

𝐌𝐲 𝐒𝐞𝐜𝐫𝐞𝐭 𝐓𝐚𝐥𝐞𝐧𝐭 — 𝐇𝐒𝐑 𝐄𝐝𝐢𝐭𝐢𝐨𝐧

• characters — Jing Yuan ; Aventurine ; Dan Heng ; GN Reader

• synopsis — I made this post, stating I can describe any fictional characters cock in detail. As promised, here is the first batch of characters requested.

• tags & warnings — smut, blow jobs, penetrative sex, hand jobs.

• a/n — The first batch is done, next up HOTD men. Requests are open! I also cut some from Aventurine because I wrote like double the amount for him, but didn’t wanna show favoritism, haha. 

Main Masterlist | Other Parts

— 𝐉𝐢𝐧𝐠 𝐘𝐮𝐚𝐧

Long - Thick - and Veiny 

There isn’t much about Jing Yuan that is disappointing, certainly not his cock. Heavy and thick, he loves nothing more than watching you drag your tongue up the long vein on the underside of his manhood. 

His fingers lace in your hair as he guides your ministrations. When you finally take him into your mouth, you can’t help but moan as the salty flavor spreads across your taste buds. Jing Yuan’s eyes glow golden, enraptured by the sight. 

Your eyes water as you take as much of him as you can, your fingers coming to wrap around the rest you can’t fit. When he finally comes, it’s creamy and viscous filling your mouth and seeping from your lips, dripping down his length as you struggle to swallow around him. 

— 𝐀𝐯𝐞𝐧𝐭𝐮𝐫𝐢𝐧𝐞

Average Sized - Curved Upward - Sensitive Tip

Size doesn't matter, and it's not that he’s lacking, but god he knows how to use what he has. Aventurine is a moderate size, but he still has you seeing stars. Together you come undone, as if he were made for you. It doesn’t matter how he takes you, his cock seemingly magic, hitting every spot just right, dragging orgasm after orgasm from your shaking body. The tip of his cock ruts against the swell of your g-spot, the curve allowing him to drag across it in a way that drives you delirious.

Aventurine loves to tease you, swapping his tip against your dripping entrance, sliding it in just enough to hear you moan before pulling out. He could cum just from this, his tip happily nestled within your walls, but he holds out, loving nothing more than hearing you whine for more. 

— 𝐃𝐚𝐧 𝐇𝐞𝐧𝐠

Long - Thick At The Base - Reactive Cock

Dan Heng could watch you play with his cock all day. Your fingers wrap around the thick base of his shaft, slowly gliding up until you incircle the tip with your thumb. A smile spreads across your face as you watch the sticky pre-cum life with your digit. Dan Heng was a silent lover, often suppressing his moans into a throaty whimper. 

It’s when he watches you lick your thumb—cleaning his essence with a satisfied hum—that his cock twitches in excitement. Even if he doesn’t utter his desires in the heat of the moment, it’s the way his breath hitches and his face flushes that has you realizing just how much he’s coming undone.

© 2024 v3nomly do not plagiarize, translate, or repost my writing to any other site.

[ohnothisisathing]

Because think of the Baghera that believed so strongly in the goodness of others and the power of community that she wanted to help Walter Bob with his work to make it easier for him and get him a hat and go to a bar. Then think of the Baghera after the reveal of her past makes her question her views on authority, where she belongs, and her very personhood all with daughter missing and her trusted friends having lost themselves. Then think of the Baghera post-Purgatory who didn’t really believe in anything but chaos and violence. She felt alone after her sense of community was warped into a toxic incircle she trauma bonded with and the others grew out of it and she did not because after everything it was all she had that made her feel like person with a family and a place to belong and not an experiment of the Federation that didn’t matter any more than the rest of the experiments that they disposed of like trash. She never really processed any of it and it hurts remembering how strong her convictions and sense of morality was.

[slycooperconfessions]

"I unironically want to know whoever it was that decided to devote a chunk of the limited space of a PS2 game into having completely unnecessary but unbelievably fun floaty fluffy tail rigging and physics, and kiss them on the mouth for making some of the most memorable bits of idle animation even to this date."

Confessed by: Anonymous

(I'm glad it's not just me!! I would sit and watch the tail and walk incircles slowly to see it twirl around!! - Mod)

[aliyalala]

gojo x small reader (BECAUSE EVERYTHING LOOKS BIG ON THIS GIRLIE BEHEHEH)

so... you decided to wear his hoodie. LORD gojo was sure he was about to faint when he saw you wearing it when he got home from work.  there you were, on the couch, with the 6 o’clock news on and dinner set out on the coffee table for the two of you.

immediately, gojo slipped next to you on the sofa and dropped his head onto your chest, inhaling your scent that currently mingled with his own.  oh your big baby was so whipped for you in his clothes~ you smiled down at him and patted his head softly. “Hi baby~” you giggled when he wrapped his arms around your stomach and looked up at you with a tired smile. “you look gorgeous in my clothes mama~” he replied (With RIZZ) you felt your cheeks heat up and his smile widened to a grin.  you felt his hands slip under his (your) hoodie and incircle your waist with his hands. just the feel of his hands on you was enough to make you melt, a quiet whine leaving your mouth when he squeezed you a bit. you felt his laugh rumble through your chest but when gojo looked up, his eyes were filled with adornment for you. he lived just to make you happy, just to be able to love you and hold you was more than gojo’s childish self could handle.  gojo reached for your lips and you leaned down to happily accept his lips on your own. the moan he let out into your mouth had your thighs squeezing around him, and returning a needy whine into his mouth. after a moment, gojo pulled back, a dazed expression on his face, cheeks flushed and saliva dripping from his lips.  “aww my angel~ you sound so pretty, you know?” you flushed even more and pushed him off of you in embarrassment. he laughed and reached for you hand, pressing his lips to it. you smiled back at him. he had such an infectious smile. “eat before dinner gets too cold, ok?” you suggested, nodding to the plates on the coffee table. he hummed in agreement. “sure mama~”

OMG thank you for all the love on my previous posts!!! rebolgs and notes are always appreciated <3 thx babes YALL ARE KEEPING ME ALIIVVE BEHEHEHHEHEHEH IF YALL GOT SOME REQUEST LMK <333

[loriandcompanyshow]

https://rumble.com/v2vwxom-i.c.u.-guide-tlc-time-911-annual-memorial-festival-benefit.html

[squareallworthy]

Triangle Tuesday 8: the nine-point circle, the deep lore, and did I say nine? I meant, like, fifty-six.

Today we are looking at the nine-point circle, a famous construction with connections to other triangle geometry that we've looked at before. But first, I'd like to re-introduce the centers that we've met so far. You should imagine that they're members of a super team each with their own little sequence that the cartoon always shows when they go into action.

And imagine that they're appearing with one of these dramatic cartoon backgrounds like this. I would go ahead and do that, but it would look really messy on the little screen you're staring at. It will look better in your imagination.

Anyway, here we go. Here they are, now each with its own thematic color.

G, the Centroid!

Secret origin: intersection of the medians

Trilinear coordinates: 1/a : 1/b : 1/c

Affiliations: Euler line, isogonal conjugate of the symmedian point

Super powers: center of gravity of triangle area • center of gravity of triangle vertices • divides triangle into equal parts ABG, BCG, and ACG • divides medians 2/3 of the distance from vertex to midpoint

O, the Circumcenter!

Secret origin: intersection of the perpendicular bisectors

Trilinear coordinates: cos A : cos B : cos C

Affiliations: Euler line, isogonal conjugate of the orthocenter

Super powers: center of circumcircle • circumcircle is locus of points with degenerate pedal triangles • relates to incenter via Euler's theorem in geometry

H, the Orthocenter!

Secret origin: intersection of the altitudes

Trilinear coordinates: sec A : sec B : sec C

Affiliations: Euler line, isogonal conjugate of the circumcenter

Super powers: constitutes an orthocentric system along with the vertices • incenter of orthic triangle • sides of orthic triangle are antiparallel to sides of reference triangle • concyclic with a vertex and two adjacent feet of altitudes

I, the incenter!

Secret origin: intersection of the angle bisectors

Trilinear coordinates: 1 : 1 : 1

Affiliations: entourage of excenters

Super powers: center of the incircle • isogonally self-conjugate • forms orthocentric system along with excenters • relates to circumcenter via Euler's theorem in geometry • always lies in interior of orthocentroidal disc

K, the symmedian point!

Secret origin: intersection of the symmedians

Trilinear coordinates: a: b: c

Affiliations: isogonal conjugate of centroid

Super powers: perspector of reference and tangential triangles • parallels through K intersect sides in six concyclic points • antiparallels through K intersect sides in six concyclic points, with K at the center of the circle • circles through K and two vertices intersect sides in six concyclic points • lines joining midpoints of altitudes and sides pass through K • centroid of its own pedal triangle • just very pretty

So now that we've got the super team together, it's time to introduce them to someone new. I know, you're thinking we've got this established cast of characters, and they relate to each other in so many varied and intimate ways. How could a new triangle fit into these relationships? Wouldn't it feel like a superfluous add-on at this point in the show?

Well, let's see. Let's go back and look at the midpoints of the sides. We find the midpoints by drawing perpedicular bisectors on each side. Those lines meet at the circumcenter, which makes the midpoints the feet of the circumcenter. The triangle formed by the midpoints is the pedal triangle of the circumcenter.

Any three points also determine, naturally, a circle. The circle formed by the feet of a point is called the pedal circle of the point. And every point has a pedal circle with respect to a given triangle.

The orthocenter, for instance, has a pedal circle defined by the feet of the altitudes, and guess what? It's the same circle! What's more, this circle bisects the segments that join the orthocenter with the vertices. For this reason, the circle is called the nine-point circle, and its center is the nine-point center, N. Let's prove that it exists.

Theorem: in any triangle the midpoints of the sides, the feet of the altitudes, and the midpoints of the segments connecting the orthocenter to the vertices lie on a common circle.

Here's our triangle ABC, with midpionts of sides Ma, Mb, Mc, feet of the altitudes Ha, Hb, Hc, and midpoints of segments joining H and the vertices Sa, Sb, Sc. We will rely on the fact that a line segment joining the midpoints of two sides (a midline) is parallel to the third side and half as long.

In green we have horizongal segments MbMa, a midline of ABC, and SaSb, a midline of ABH. Both of these midlines are parallel to side AB and half its length, so they are parallel to each other and equal. Vertical green segments MbSa and MaSb are midliness of ACH and BCH respectively, so they are also parallel and equal. Therefore the green segments form a rectangle.

In the same way, the blue segments also form a rectangle. These two rectangles have a common diagonal MbSb, and so have the same circumcircle. And McHcSc is a right triangle, and its hypotenuse McSc is also a diagonal of the blue rectangle. Therefore Hc is on the same circle, and by analogous argument so are Ha and Hb.

Since now we can be sure the nine-point circle and its center exist, it should get its own introduction scene and signature color.

N, the nine-point circle!

Secret origin: pedal circle of circumcenter and orthocenter

Trilinear coordinates: cos(B-C) : cos(C-A) : cos(A-B)

Affiliations: Euler line

Super powers: passes through nine points • many many others which we will get to next

So those are some nice ways that connect the nine-point circle to the circumcenter and orthocenter. And it's cool that this new character N has some connections to the established characters O and H, but what about the other points? Can we find some connections there?

Yes, we can, because it turns out the nine-point center is connected to everything. Would you like to see some of them?

(This is me right now.)

Because there are kind of a lot.

The nine-point circle is tangent to the incircle and the excircles. If you are keeping track, that's now 13 points of interest on the nine-point circle.

The radius of the nine-point circle is half that of the circumcircle. This is easy to see, because the circle is the circumcircle of the medial triangle, which is half the size of the reference triangle.

The nine-point center lies on the Euler line midway between the circumcenter and the orthocenter. The centroid is one-third of the way from the circumcenter to the orthocenter. These positions give the orthocenter and centroid special status with regard to the nine-point circle.

The nine-point circle bisects any line segment from the orthocenter to the circumcircle, making the fact that it bisects the tops of the altitudes into a special case of a general property.

The centroid trisects any line segment extending from a point on the nine-point circle through G and on to the circumcircle. Another way of saying this is that G is a center of dilation between the circumcircle and nine-point circle with scaling factor -1/2. In triangle geometry, this particular dilation through G is called taking the complement of a point, so a third way of describing this relationship is to say that the nine-point circle is the complement of the circumcircle.

The nine-point center is also the center of gravity of A, B, C, and H.

As we have seen previously, the vertices and the orthocenter form an orthocentric system, meaning that any one of the points A, B, C, and H is the orthocenter of the other three. For all four of the triangles ABC, ABH, ACH, and BCH, the feet of the altitudes are the same, so they all share the same orthic triangle and the same nine-point circle.

But each of these four triangles has its own incircle and set of excircles, and the nine-point circle is tangent to all of them, making sixteen points of tangency. That's now 29 points of interest on the nine-point circle.

The incenter and the excenters form another orthocentric system, and the nine-point center of this system is the circumcircle of the original triangle. The reference triangle ABC is the orthic triangle of the excentral triangle JaJbJc.

And speaking of the orthic triangle, it defines three other triangles in the corners that are similar to the reference triangle. The Euler lines of these corner triangles coincide at a point on the nine-point circle. That brings us to 30 points of interest on the nine-point circle.

Let's go back to pedal triangles, and remember that if a point is on the circumcircle, its feet are colinear and its pedal triangle has collapsed to a line segment, called a Simson line. The envelope of these line segments form a shape called the Steiner deltoid.

The nine-point center is also the center of the Steiner deltoid, and the circle is tangent to the deltoid at three points. There are four different circumcircles in an orthocentric system, so there are twelve points of tangency in all, so we now have 42 points of interest on the nine-piont circle.

The Simson lines of two opposite points on the circumcircle intersect perpendicularly on the nine-point circle.

You may have noticed that in citing all these connections I haven't mentioned the symmedian point K so far. As far as I can tell, K is just not that very strongly connected to N. However, here's one: the circle through K, N, and O is orthogonal to the circle with diameter GH (the orthocentroidal circle). That's five members of our super team tied into one relation. But that's all I've got. Sometimes members of a team don't interact that much.

And this is the kind of thing you look for in a successful series, right? You have an established cast of characters, with a rich, dense lore linking them all together in various ways. Then, as the story develops and someone new is introduced, new retlationships make the lore even richer. That that's why I'm in the triangle fandom.

With that, I think the only question left to answer is "Hey, Square, do you happen to have a group portrait of the whole team together in one clear and not at all confusing picture?" And of course I do.

If you found this interesting, please try drawing some of this stuff for yourself! You can use a compass and straightedge, or software such as Geogebra, which I used to make all my drawings. You can try it on the web here or download apps to run on your own computer here.

An index of all posts in this series is available here.

[icubuzz]

Here is an example of just how cool this platform is. My Company B and the entire Team Resolute team gets a special discount and help. https://www.canva.com/design/DAEniT8NwUM/8L7Eh3l3nWNuowRWV915xg/watch