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### EGMO 2013/1

Posted: Sun Feb 04, 2018 11:08 pm
The side $BC$ of $\triangle ABC$ is extended beyond $C$ to $D$ so that $CD = BC$.The side $CA$ is extended beyond $A$ to $E$ so that $AE = 2CA$.
Prove that if $AD = BE$, then $\triangle ABC$ is right-angled.

### Re: EGMO 2013/1

Posted: Sun Feb 04, 2018 11:17 pm

### Re: EGMO 2013/1

Posted: Mon Dec 03, 2018 3:26 pm
Join D,E.Let AD meets BE at M.
Now, C is the midpoint of BD and
EA:AC=2:1. So, A if the centroid of triangle EDB . So, M is the midpoint of BE. BM=EM=BE/2.