# A Parallelogram Defined by the Centers of Four Incircles

A Parallelogram Defined by the Centers of Four Incircles

Let ABC be a triangle. Let the line DEF be parallel to AC with D on AB and E on BC. Let the line FGH be parallel to AB with H on AC and G on BC. Let O, , , and be the incircles of the triangles ABC, DBE, FEG, and CGH, respectively. Then O is a parallelogram.

O

1

O

2

O

3

O

1

O

2

O

3