MathDB

A circle touches sides

DA

AB

BC

CD

of a quadrilateral

ABCD

at points

K

L

M

N

, respectively. Let

S_1

S_2

S_3

S_4

respectively be the incircles of triangles

AKL

BLM

CMN

DNK

. The external common tangents distinct from the sides of

ABCD

are drawn to

S_1

and

S_2

S_2

and

S_3

S_3

and

S_4

S_4

and

S_1

. Prove that these four tangents determine a rhombus.

Problem Statement