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