MathDB

In a convex qualrilateral

ABCD

, let

P

be the intersection point of

AD

and

BC

. Suppose that

I_1

and

I_2

are the incenters of triangles

PAB

and

PDC

,respectively. Let

O

be the circumcenter of

PAB

, and

H

the orthocenter of

PDC

. Show that the circumcircles of triangles

AI_1B

and

DHC

are tangent together if and only if the circumcircles of triangles

AOB

and

DI_2C

are tangent together. Proposed by Hooman Fattahimoghaddam

Problem Statement