Problem 351. Rhombus, Incircles, Common tangent, Circumscribable or
Tangential quadrilateral. Level: High School, College, SAT Prep.
The figure shows a rhombus 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).
Geometry problem solving
Geometry problem solving is one of the most challenging skills for students to learn. When a problem requires auxiliary construction, the difficulty of the problem increases drastically, perhaps because deciding which construction to make is an illstructured problem. By “construction,” we mean adding geometric figures (points, lines, planes) to a problem figure that wasn’t mentioned as "given."

Recent Additions
