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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 inradii
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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