Question

A triangle has corners at `(5 ,8 )`, `(3 ,9 )`, and `(4 ,7 )`. What is the area of the triangle's circumscribed circle?

Answer 1

the area of the circle inscribed = 0.8160

Explanation:

the triangle is isoceles, side lengths = `sqrt5, sqrt5 and sqrt2`
triangle area (A) = `1/2xxsqrt2xx3/sqrt2=3/2`
triangle perimeter (P) = `sqrt5+sqrt5+sqrt2=2sqrt5+sqrt2=5.8863`
inradius (r) =`(2A)/P` =`2xx1.5/5.8863=0.50965`
area of the circle = `pixxr^2 = pixx(0.50965)^2`
`=0.8160`