In the figure below, given a triangle
ABC of area S, s is the semiperimeter (a + b + c) / 2, and ra
is the exradius relative to side BC. Prove that S = ra.(s
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. AREA OF A TRIANGLE:
The area of a triangle equals one-half the product of the length
of a side and the length of the altitude to that side.