Let me study those curves of yours

by shiningsunnyday, Oct 30, 2016, 4:24 AM

Euclidean Geometry in Mathematical Olympiads wrote:
Let $ABC$ be a triangle and $D$ be a point on $AB$. Suppose a circle $\omega$ is tangent to $CD$ at $L, AB$ at $K$, and also to $(ABC).$ Then the incenter of $ABC$ lies on line $LK.$

Note that the circle is better-known as a curvilinear incircle of $ABC,$ a special case of which is the A-mixtilinear incircle.
Solution
Tidbit
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6 Comments

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wowowowowow the clickbait titles are real

by phi_ftw1618, Oct 30, 2016, 4:39 AM

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"$CLIT$ is cyclic"
O_O Whoa there... AoPS is supposed to be open for all ages...

by zephyrcrush78, Oct 30, 2016, 4:51 AM

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It's funny how on Page 69 of all pages has "Quadrilaterals $BKIT$ and $\mathbf{CLIT}$ are concyclic."
I am directly quoting the text here (except for the bolded part but the text is verbatim).

by zephyrcrush78, Oct 30, 2016, 5:31 AM

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AoPS is PG guys come on

by agbdmrbirdyface, Oct 31, 2016, 1:18 AM

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I was just quoting v_Enhance's book and shiningsunnyday's solution, no changes whatsoever (except for the bold) >_>

by zephyrcrush78, Oct 31, 2016, 1:19 AM

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:what?:

huh I wonder if v_Enhance knows about this

by Wiggle Wam, Nov 2, 2016, 7:56 PM

To share with readers my favorite problem I came across today :) (Shout for contrib.)

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  • this guy is an absolute legend. much love wherever you are Michael

    by LeonidasTheConquerer, Aug 5, 2024, 9:37 PM

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  • orzorzorzorzorzorozo

    by samrocksnature, Jul 16, 2021, 8:25 PM

  • 2021 post

    by the_mathmagician, May 5, 2021, 3:28 PM

  • Let $ ABC$ be an equilateral triangle of side length $ 1$. Let $ D$ be the point such that $ C$ is the midpoint of $ BD$, and let $ I$ be the incenter of triangle $ ACD$. Let $ E$ be the point on line $ AB$ such that $ DE$ and $ BI$ are perpendicular. $ \

    by ARay10, Aug 25, 2020, 5:55 PM

  • Nice blog! :)

    by User526797, Jan 12, 2020, 4:48 PM

  • oh my gosh it's been so longggggg.... contrib? what does that mean?

    by adiarasel, Dec 1, 2019, 8:31 PM

  • 2019 post

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  • hi contrib please

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  • contrib /charmander

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  • for contrib

    by SomethingNeutral, Mar 30, 2017, 7:57 PM

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