MathDB

Two circles

\alpha{}

and

\beta{}

with centers

A{}

and

B{}

respectively intersect at points

C{}

and

D{}

. The segment

AB{}

intersects

\alpha{}

and

\beta{}

at points

K{}

and

L{}

respectively. The ray

DK

intersects the circle

\beta{}

for the second time at the point

N{}

, and the ray

DL

intersects the circle

\alpha{}

for the second time at the point

M{}

. Prove that the intersection point of the diagonals of the quadrangle

KLMN

coincides with the incenter of the triangle

ABC

.
Konstantin Knop

Problem Statement