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In the figure below, given a
triangle ABC, line DEF parallel to AC and line FGM parallel to
AB. If R, R1, R2, and R3, are the circumradii
of triangles ABC, DBE, FGE, and MGC respectively, prove that R = R1
+ R2 + R3.
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FACTS AND HINTS:
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."
1. SIMILAR TRIANGLES:
Proposition:
Corresponding segments of similar triangles are in proportion.
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