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

1 Answer
Jan 14, 2017

(65pi)/2

Explanation:

First, use the formula for area of triangle=1/2 [x_1 (y_2 -y_3)+x_2 (y_3 -y_1) +x_3 (y_1 -y_2)]
=1/2[6(6-6)+7(6-4)+3(4-6]= 8

Next find the side lengths using distance formula. The sides would be sqrt( (6-7)^2 +(4-6)^2)= sqrt5,
sqrt((7-3)^2 +(6-6)^2)= sqrt16
and sqrt((6-3)^2 +(4-6)^2)= sqrt 13

Now use the formula R= (abc)/(4Delta) to get the radius R of the circumcircle of the triangle, where a,b,c aree its sides and Delta is the area of the triangle.

Accordingly, R=(sqrt5 sqrt16 sqrt13)/(4(8))

Area of the circumcircle would thus be pi R^2

= (pi (5)(13)(16))/32= (65pi)/2