MathDB

Let

ABC

be an arbitrary triangle. On the perpendicular bisector of

AB

, there is a point

P

inside of triangle

ABC

. On the sides

BC

and

CA

, triangles

BQC

and

CRA

are placed externally. These triangles satisfy

\vartriangle BPA \sim \vartriangle BQC \sim \vartriangle CRA

. (So

Q

and

A

lie on opposite sides of

BC

, and

R

and

B

lie on opposite sides of

AC

.) Show that the points

P, Q, C

and

R

form a parallelogram.

Problem Statement