×

# 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

## Comments

Sort by:

Top Newest

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

Log in to reply

· 1 month ago

Log in to reply

Triangle LDC ~~ triangle BDK by SAS similarity criteria . · 1 month ago

Log in to reply

I forgot to mention something · 1 month ago

Log in to reply

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

Log in to reply

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. · 1 month ago

Log in to reply

sorry its the opposite · 3 weeks, 6 days ago

Log in to reply

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

Log in to reply

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

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...