MathDB

A convex quadrilateral

ABCD

has an inscribed circle with center

I

. Let

I_a, I_b, I_c

and

I_d

be the incenters of the triangles

DAB, ABC, BCD

and

CDA

, respectively. Suppose that the common external tangents of the circles

AI_bI_d

and

CI_bI_d

meet at

X

, and the common external tangents of the circles

BI_aI_c

and

DI_aI_c

meet at

Y

. Prove that

\angle{XIY}=90^{\circ}

G7