MathDB

Let the points

M

and

N

be the intersections of the inscribed circle of the right-angled triangle

ABC

, with sides

AB

and

CA

respectively , and points

P

and

Q

respectively be the intersections of the ex-scribed circles opposite to vertices

B

and

C

with direction

BC

. Prove that the quadrilateral

MNPQ

is a cyclic if and only if the triangle

ABC

is right-angled with a right angle at the vertex

A

Problem Statement