Simson says... go do geo!

by shiningsunnyday, Dec 10, 2016, 4:02 AM

2014 USA Dec. TST P1 wrote:
Let $ABC$ be an acute triangle, and let $X$ be a variable interior point on the minor arc $BC$ of its circumcircle. Let $P$ and $Q$ be the feet of the perpendiculars from $X$ to lines $CA$ and $CB$, respectively. Let $R$ be the intersection of line $PQ$ and the perpendicular from $B$ to $AC$. Let $\ell$ be the line through $P$ parallel to $XR$. Prove that as $X$ varies along minor arc $BC$, the line $\ell$ always passes through a fixed point.

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Have you done 2013 TSTST #1, that is also Simson Lines?

Hm interesting I'll check it out later
This post has been edited 1 time. Last edited by shiningsunnyday, Dec 10, 2016, 11:23 PM

by First, Dec 10, 2016, 2:11 PM

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

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