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How to prove that in every triangle the segment $OJ=KL$

Discussion in 'Mathematics' started by endgame endgame, Aug 2, 2020 at 2:25 AM.

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    given a $\triangle ABO$, there are 3 squares with side length $AB,BO$ and $OA$ on the sides of the triangle. $K, L$ and $J$ are the centers of the squares. How to prove that the segment$OJ=KL$, and also how to prove $OJ\perp KL$. i don't know how to start. i think this is the generalization of Van Aubel's theorem. any hints

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