Problem 352. Tangential quadrilateral, Incircles, Common tangent,
Circumscribable or Tangential quadrilateral.
The figure shows a tangential
quadrilateral ABCD with a point E on side BC. Circles 1 and 2
are the incircles of triangles ABE and CDE, respectively. FG is
the common tangent to circles 1 and 2. FG intersects to AE and
DE at M and N, respectively. Prove that the quadrilateral AMND
is circumscribable or tangential (sides all lie tangent to a
single circle inscribed within the quadrilateral).

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