MathDB

Let

ABC

be a triangle . Let

A'

be the center of the circle through the midpoint of the side

BC

and the orthogonal projections of

B

and

C

on the lines of support of the internal bisectrices of the angles

ACB

and

ABC

, respectively ; the points

B'

and

C'

are defined similarly . Prove that the nine-point circle of the triangle

ABC

and the circumcircle of

A'B'C'

are concentric.

Problem Statement