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Online Geometry Problem 885: Three Intersecting Circles, Three Tangent Lines, Midpoint. Level: High School, Honors Geometry, College, Mathematics Education

In the diagram below, the circles A and B intersect at C and D. CE is tangent to circle A at C, CF is tangent to circle B at C, circle G passes through the points C, E, F. If HM is tangent to circle G at C, prove that C is the midpoint of HM.

Geometry Problem: Three Intersecting Circles, Three Tangent Lines, Midpoint



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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