MathDB

Let

ABC

be a triangle such that

AC>AB.

A circle tangent to the sides

AB

and

AC

D

and

E

respectively, intersects the circumcircle of

ABC

K

and

L

. Let

X

and

Y

be points on the sides

AB

and

AC

respectively, satisfying \frac{AX}{AB}=\frac{CE}{BD+CE} \text{and} \frac{AY}{AC}=\frac{BD}{BD+CE} Show that the lines

XY, BC

and

KL

are concurrent.

Problem Statement