MathDB

Let

\Gamma

be the circumcircle of a triangle

ABC,

and let

D

and

E

be two points different from the vertices on the sides

AB

and

AC,

respectively. Let

A'

be the second point where

\Gamma

intersects the bisector of the angle

BAC,

and let

P

and

Q

be the second points where

\Gamma

intersects the lines

A'D

and

A'E,

respectively. Let

R

and

S

be the second points of intersection of the lines

AA'

and the circumcircles of the triangles

APD

and

AQE,

respectively. Show that the lines

DS, \: ER

and the tangent line to

\Gamma

through

A

are concurrent.

Problem Statement