MathDB

Let

ABC

be a triangle with

AH

altitude. The point

K

is chosen on the segment

AH

as follows such that

AH =3KH

. Let

O

be the center of the circle circumscribed around by triangle

ABC, M

and

N

be the midpoints of

AC

and AB respectively. Lines

KO

and

MN

intersect at the point

Z

, a perpendicular to

OK

passing through point

Z

intersects lines

AC

and

AB

at points

X

and

Y

respectively. Prove that

\angle XKY =\angle CKB

Problem Statement