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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