MathDB

2012 ToT Spring Junior O p3 rectangle wanted, 4 incircles, parallelogram

Source:

March 4, 2020

geometryrectangleparallelogramincircle

Problem Statement

In the parallelogram

ABCD

, the diagonal

AC

touches the incircles of triangles

ABC

and

ADC

W

and

Y

respectively, and the diagonal

BD

touches the incircles of triangles

BAD

and

BCD

X

and

Z

respectively. Prove that either

W,X, Y

and

Z

coincide, or

WXYZ

is a rectangle.