In the figure below, given a triangle
ABC of area S, s is the semiperimeter (a + b + c) / 2, and r is
the inradius.
Prove that S = s.r
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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 illstructured problem. By
“construction,” we mean adding geometric figures
(points, lines, planes) to a problem figure that
wasn’t mentioned as "given."
1. AREA OF A TRIANGLE:
Proposition:
The area of a triangle equals onehalf the product of the length
of a side and the length of the altitude to that side.
