MathDB

Given an acute-angled triangle

ABC

and a point

P

inside it such that

\angle PBA=\angle PCA

. The lines

PB

and

PC

intersect the circumcircles of triangles

PCA

and

PAB

secondly at points

M

and

N

, respectively. Let the rays

MC

and

NB

intersect at a point

S

K

is the center of the circumscribed circle of the triangle

SMN

. Prove that the lines

AK

and

BC

are perpendicular.

Problem Statement