MathDB

Given a triangle

ABC

in which the angle

B

is equal to

60^\circ

. A circle inscribed in a triangle with a center

I

touches the side

AC

at point

K

. A line passing through the points of touching of this circle with the other sides of the triangle intersects the its circumcircle at points

M

and

N

. Prove that the ray

KI

divides the arc

MN

in half.

Problem Statement