EGMO 2013 Problem 1

Day 1
Answer

The side $B C$ of the triangle $A B C$ is extended beyond $C$ to $D$ so that $C D=B C$ . The side $C A$ is extended beyond $A$ to $E$ so that $A E=2 C A$ .

Prove that if $A D=B E$ , then the triangle $A B C$ is right-angled.

Dataset text NuminaMath olympiads. Quoted with source.

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a^{2}=b^{2}+c^{2}

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