MathDB

Fixed points

B

and

C

are on a fixed circle

\omega

and point

A

varies on this circle. We call the midpoint of arc

BC

(not containing

A

)

D

and the orthocenter of the triangle

ABC

H

. Line

DH

intersects circle

\omega

again in

K

. Tangent in

A

to circumcircle of triangle

AKH

intersects line

DH

and circle

\omega

again in

L

and

M

respectively. Prove that the value of

\frac{AL}{AM}

is constant.
Proposed by Mehdi E'tesami Fard

Problem Statement