Problem 348. Circles, Common External Tangents, Common Internal
Tangent.
Level: High School, College.
The figure shows circles A and B with the common external
tangents CD and EF and the common internal tangent GH. If M and
N are the tangency points, prove that GM = HN.
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." 
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