Area of Inscribed Circle

The perimeter and area of a triangle are 20 inches and 12 square inches, respectively. What is the area in square inches of a circle inscribed in the triangle?
Source: NCTM Mathematics Teacher, February 2006

SOLUTION
image
area of AIB=(1/2)cr\qquad (1)
area of BIC=(1/2)ar\qquad (2)
area of AIC=(1/2)br\qquad (3)
Add all three equations
area of ABC=(1/2)r(a+b+c)
12=(1/2)r(20)
r=6/5
Area of inscribed circle
\pi(6/5)^2=1.44\pi

Answer: 1.44\pi square inches

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About mvtrinh

Retired high school math teacher.
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