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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).

Rhombus, Incircles, Tangential quadrilateral 



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 ill-structured problem. By “construction,” we mean adding geometric figures (points, lines, planes) to a problem figure that wasn’t mentioned as "given."

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