Problem 355. Circles, Common external tangent, Concyclic points.
Level: High School, College, SAT Prep.
The figure shows circles 1 and 2 with
the common external tangents ABCD and EFGH. Circle 1 is tangent
to BF at M and circle 2 is tangent to CG at N. Lines AM and DN
meet at P and lines EM and HN meet at Q. Prove that the points
M, P, N, and Q are concyclic (lie on a same circle).
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."