MathDB

A triangle

ABC

with an obtuse angle at the vertex

C

is inscribed in a circle with a center at point

O

. Circumcircle of triangle

AOB

centered at point

P

intersects line

AC

at points

A

and

A_1

, line

BC

at points

B

and

B_1

, and the perpendicular bisector of the segment

PC

at points

D

and

E

. Prove that points

D

and

E

together with the centers of the circumscribed circles of triangles

A_1OC

and

B_1OC

lie on one circle.

Problem Statement