## 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

area of $AIB=(1/2)cr\qquad (1)$
area of $BIC=(1/2)ar\qquad (2)$
area of $AIC=(1/2)br\qquad (3)$
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