Question

A triangle has corners at `(6 ,4 )`, `(7 ,5 )`, and `(3 ,3 )`. What is the area of the triangle's circumscribed circle?

Answer 1

Area of circumscribed circle `= pi * 5.09^2 = 81.39` sq.unit

Explanation:

Sides `AB=sqrt((6-7)^2+(4-5)^2) = sqrt2=1.41`
`BC=sqrt((7-3)^2+(5-3)^2) =sqrt20=4.47`
`CA=sqrt((3-6)^2+(3-4)^2) = sqrt10=3.16`
Semi Perimeter:`s=(1.41+4.47+3.16)/2=4.52`
Area of triangle:`A=sqrt(4.52(4.52-1.41)(4.52-4.47)(4.52-3.16))=0.977`
Radius of circle:`R=(AB*BC*CA)/(4*A) = (1.41*4.47*3.16)/(4*0.977)=5.09 :.`Area of circle `= pi * 5.09^2 = 81.39` sq.unit [Ans]