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RMO 2016

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

Note by Neel Khare
1 month, 1 week ago

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What have you tried? What do you know? Calvin Lin Staff · 1 month, 1 week ago

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@Calvin Lin

Rohit Camfar · 1 month ago

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@Rohit Camfar Triangle LDC ~~ triangle BDK by SAS similarity criteria . Vishwash Kumar · 1 month ago

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@Rohit Camfar I forgot to mention something Vishwash Kumar · 1 month ago

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@Vishwash Kumar i have already proved this you have to also prove the converse. that is not easy Neel Khare · 1 month ago

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@Neel Khare In your below post to calvin Lin , You had said that it is easy to 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 · 1 month ago

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@Rohit Camfar sorry its the opposite Neel Khare · 3 weeks, 6 days ago

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@Neel Khare Messed up , but couldn't do it. Have you any idea ? Vishwash Kumar · 3 weeks, 6 days ago

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@Calvin Lin it is easy to prove that angle BAC=90 if B,K,C,L are concyclic the converse is not that easy. Neel Khare · 1 month, 1 week ago

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