A triangle has corners at #(9 ,4 )#, #(3 ,2 )#, and #(5 ,8 )#. What is the area of the triangle's circumscribed circle?

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Answer 1 · 2018-06-29T07:56:15

#color(orange)("Area of Circum circle " A_R = pi R^2 = 39.27 " sq units"#

#"Area of Triangle " = A_T = (a b c) / (4 R)#

#A (9,4), B (3,2), C(5,8)#

#a = sqrt((5-3)^2 + (8-2)^2) = sqrt 40 = 6.3246#

#b = sqrt((5-9)^2 + (8-4)^2) = sqrt 32 = 5.6569#

#c = sqrt((9-3)^2 + (2-2)^2) = sqrt 40 = 6.3246#

#"Semi perimeter of the triangle " s = (a + b + c ) / 2 = 9.153#

#A_T = sqrt s (s-a) (s-b) (s - c))#

#A_T = sqrt(9.153 (9.153 - 6.3246) (9.153 - 5.6569) (9.153 - (6.3246)) = 16#

#R = (a b c ) / (4 * A_T) = (sqrt40 * sqrt32* sqrt40) / (4 * 16) = 3.5355#

#color(orange)("Area of Circum circle " A_R = pi R^2 = pi * 3.5355^2 = 39.27 " sq units"#