MathDB

Let

\omega

denote the circumscribed circle of an acute-angled

\triangle ABC

with

AB \neq BC

. Let

A'

be the point symmetric to the point

A

with respect to the line

BC

. The lines

AA'

and

A'C

intersect

\omega

for the second time at points

D

and

E

, respectively. Let the lines

AE

and

BD

intersect at point

P

. Prove that the line

A'P

is tangent to the circumscribed circle of

\triangle A'BC

.
Proposed by Oleksii Masalitin

Problem Statement