MathDB

In a non-isosceles acute triangle

ABC

D

is the midpoint of the edge

[BC]

. The points

E

and

F

lie on

[AC]

and

[AB]

, respectively, and the circumcircles of

CDE

and

AEF

intersect in

P

[AD]

. The angle bisector from

P

in triangle

EFP

intersects

EF

Q

. Prove that the tangent line to the circumcirle of

AQP

A

is perpendicular to

BC

Problem Statement