Revisiting a September 2016 Problem

by tastymath75025, Apr 16, 2017, 4:18 AM

shiningsunnyday posted this problem on his blog in september but never finished his solution :mad:

Let $O$ be the circumcenter of an acute-angled triangle $ABC$, and let $M$ be a point on the circumcircle of $ABC$. Let $X,Y,Z$ be the projections of $M$ onto $OA,OB,OC$ respectively. Prove that the incenter of $XYZ$ lies on the Simson line of $M$ with respect to $ABC$.

solution

tidbit
geometry

Comment

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3 Comments

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ssd, I find your lack of faith disturbing.

by MathAwesome123, Apr 16, 2017, 4:20 AM

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darn, what are computationts?

by MathStudent2002, Apr 16, 2017, 5:00 AM

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@MathStudent2002 stole my comment :mad:

by hwl0304, Apr 16, 2017, 2:37 PM

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

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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! :)

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

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

  • 2019 post

    by piphi, Aug 10, 2019, 6:32 AM

  • hi contrib please

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  • hihihihihi contrib plzzzzz

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  • 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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