Question

A triangle has corners at `(5 ,6 )`, `(5 ,9 )`, and `(8 ,2 )`. What is the area of the triangle's circumscribed circle?

Answer 1

Area of circumscribed circle `127.9` sq.unit

Explanation:

Sides `AB=a=sqrt((5-5)^2+(6-9)^2)=3 ; BC=b=sqrt((5-8)^2+(9-2)^2)=sqrt58=7.62; CA=c=sqrt((8-5)^2+(2-6)^2)=5`
Semi perimeter `s=(3+5+7.62)/2=7.81` Area of the triangle `A_r=sqrt (s(s-a)(s-b)(s-c))=sqrt(7.81*4.81*0.19*2.81)=4.48` circumscribed triangle radius `r=(a*b*c)/(4*A_r)=(3*7.62*5)/(4*4.48)=6.38:.`Area of circumscribed circle `A=pi*r^2=pi*6.38^2=127.9` sq.unit[Ans]