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=√(1−7)2+(1−9)2=10.0
Side BC=b=√(7−4)2+(9−2)2=7.6
Side CA=c=√(4−1)2+(2−1)2=3.16

Semi perimeter of triangle S=10.0+7.6+3.162=10.38

Area of the triangle At=√s(s−a)(s−b)(s−c)
=√10.38(10.38−10.0)(10.38−7.6)(10.38−3.16)=√79.17=8.9

Circumscribed circle radius is R=a⋅b⋅c4.At
R=10.0⋅7.6⋅3.164⋅8.9=6.74

Area of circumscribed circle is Ac=π⋅R2=π⋅6.742=143.0

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