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

1 Answer
Binayaka C.
Jun 25, 2016

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]

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