# 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
2 years, 3 months ago

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$...$$ or $...$ to ensure proper formatting.
2 \times 3 $$2 \times 3$$
2^{34} $$2^{34}$$
a_{i-1} $$a_{i-1}$$
\frac{2}{3} $$\frac{2}{3}$$
\sqrt{2} $$\sqrt{2}$$
\sum_{i=1}^3 $$\sum_{i=1}^3$$
\sin \theta $$\sin \theta$$
\boxed{123} $$\boxed{123}$$

Sort by:

What have you tried? What do you know?

Staff - 2 years, 3 months ago

- 2 years, 2 months ago

I forgot to mention something

- 2 years, 2 months ago

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

- 2 years, 2 months ago

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.

- 2 years, 2 months ago

sorry its the opposite

- 2 years, 2 months ago

Messed up , but couldn't do it. Have you any idea ?

- 2 years, 2 months ago

Triangle LDC ~~ triangle BDK by SAS similarity criteria .

- 2 years, 2 months ago

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

- 2 years, 3 months ago