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

No vote yet

1 vote

×

Problem Loading...

Note Loading...

Set Loading...

## Comments

Sort by:

TopNewestWhat have you tried? What do you know?

Log in to reply

Log in to reply

Triangle LDC ~~ triangle BDK by SAS similarity criteria .

Log in to reply

I forgot to mention something

Log in to reply

Log 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.Log in to reply

Log in to reply

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.

Log in to reply