MathDB

Let

ABC

be a triangle and let the tangent at

B{}

to its circumcircle meet the internal bisector of the angle

A{}

P{}

. The line through

P{}

parallel to

AC

meets

AB

Q{}

. Assume that

Q{}

lies in the interior of segment

AB

and let the line through

Q{}

parallel to

BC

meet

AC

X{}

and

PC

Y{}

. Prove that

PX

is tangent to the circumcircle of the triangle

XYC

Problem Statement