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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