MathDB

A circle inscribed in triangle

ABC

has center

O

and touches side

AC

at point

K

. A second circle also has center

O

, intersects all sides of triangle

ABC

. Let

E

and

F

be the corresponding points of intersection with sides

AB

and

BC

, closest to vertex

B

;

B_1

and

B_2

are the points of its intersection with side

AC

, and

B_1

is closer to

A

. Prove that points

B

K

and point

P

, the intersections of the segments

B_2E

and

B_1F

lie on the same straight line.

Problem Statement