A triangle has corners at #(9 ,3 )#, #(4 ,9 )#, and #(2 ,8 )#. What is the area of the triangle's circumscribed circle?

1 Answer
bp
Jan 10, 2017

61.34 approx

Explanation:

Radius R of the circumcircle of a triangle is given by the formula

#R= (abc)/(4Delta)# where a,b,c are the side lengths and #Delta# is the area of the triangle. The three sides of the triangle in the present case would be

#sqrt((9-4)^2 +(3-9)^2) = sqrt 61#

#sqrt((9-2)^2 +(3-8)^2)=sqrt74#

#sqrt((4-2)^2 +(9-8)^2)= sqrt5#

Area of triangle can be had using the formula
#1/2 [x_1 (y_2-y_3)+x_2(y_3-y_1)+x_2(y_1 -y_2]#

=#1/2[9(9-8) +4(8-3) +2(3-9)]#= 8.5

Radius R =#sqrt(61*74*5) /(4(8.5))#

Area of the circumcircle would be #pi (61*74*5)/34^2#= 61.34 aprox

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