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

1 Answer
Jul 30, 2016

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]