omg i haven't done geo in a month

by wu2481632, Nov 4, 2016, 3:08 PM

so rusty

Let $\Omega$ and $O$ be the circumcircle and the circumcentre of an acute-angled triangle $ABC$ with $AB > BC$. The angle bisector of $\angle ABC$ intersects $\Omega$ at $M \ne B$. Let $\Gamma$ be the circle with diameter $BM$. The angle bisectors of $\angle AOB$ and $\angle BOC$ intersect $\Gamma$ at points $P$ and $Q,$ respectively. The point $R$ is chosen on the line $P Q$ so that $BR = MR$. Prove that $BR\parallel AC$. (ISL 2014 G3)

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Why did you stop doing geometry? Your supposed to be the geometry only guy. Just kidding but anyway wu keep up doing geometry and you could make green MOP. But you probably need another subject to get away with. NT or algebra could do the trick.

by First, Nov 5, 2016, 1:40 AM

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Hmm this configuration is pretty cool - I'll take a deeper look tomorrow after I dig myself out of all the schoolwork on top of me. X_X

by shiningsunnyday, Nov 5, 2016, 3:15 PM

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

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