A triangle has corners at (1 ,1 ), (7 ,9 ), and (4 ,2 ). What is the area of the triangle's circumscribed circle?

1 Answer
Binayaka C.
Jun 2, 2017

Area of triangle's circumscribed circle is 143.0

Explanation:

Vertices of triangle are A(1,1), B(7,9) , (4,2)
Side AB=a=sqrt((1-7)^2+(1-9)^2)= 10.0
Side BC=b=sqrt((7-4)^2+(9-2)^2)= 7.6
Side CA=c=sqrt((4-1)^2+(2-1)^2)= 3.16

Semi perimeter of triangle S=(10.0+7.6+3.16)/2=10.38

Area of the triangle A_t=sqrt(s(s-a)(s-b)(s-c))
=sqrt(10.38(10.38-10.0)(10.38-7.6)(10.38-3.16)) = sqrt79.17=8.9

Circumscribed circle radius is R=(a*b*c)/(4.A_t)
R=(10.0*7.6*3.16)/(4*8.9) =6.74

Area of circumscribed circle is A_c =pi*R^2=pi*6.74^2=143.0

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