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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.

Common external, internal, tangent



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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