Let ∆ABC be scalene, with BC as the largest side. Let

D

be the foot of the altitude from

A onto side BC. Let points

K and

L be chosen on the lines AB and AC respectively,

such that

D is the midpoint of segment KL. Prove that the

points B, K, C, L are concyclic if and only if

∠BAC = 90

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## Comments

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TopNewestWhat have you tried? What do you know?

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I forgot to mention something

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easyto prove that if B,K,C,L are concyclic THEN angle BAC=90 the converse (i.e , if angle BAC =90 then B,C,K,L are concyclic ) is not that easy.Log in to reply

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Triangle LDC ~~ triangle BDK by SAS similarity criteria .

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it is easy to prove that angle BAC=90 if B,K,C,L are concyclic the converse is not that easy.

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