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

## Comments

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TopNewestWhat have you tried? What do you know? – Calvin Lin Staff · 9 months, 4 weeks ago

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– Vishwash Kumar · 9 months, 2 weeks ago

Triangle LDC ~~ triangle BDK by SAS similarity criteria .Log in to reply

– Vishwash Kumar · 9 months, 2 weeks ago

I forgot to mention somethingLog in to reply

– Neel Khare · 9 months, 2 weeks ago

i have already proved this you have to also prove the converse. that is not easyLog in to reply

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. – Rohit Camfar · 9 months, 2 weeks agoLog in to reply

– Neel Khare · 9 months, 2 weeks ago

sorry its the oppositeLog in to reply

– Vishwash Kumar · 9 months, 2 weeks ago

Messed up , but couldn't do it. Have you any idea ?Log in to reply

– Neel Khare · 9 months, 4 weeks ago

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