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

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

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Answer 1 · 2018-06-29T07:56:15

$Area of Circum circle A_{R} = π R^{2} = 39.27 sq units$ $color(orange)("Area of Circum circle " A_R = pi R^2 = 39.27 " sq units"$

Explanation:

![http://mathibayon.blogspot.com/2015/01/ derivation-of-formula-for-radius-of-circumcircle.html

$Area of Triangle = A_{T} = \frac{a b c}{4 R}$ $"Area of Triangle " = A_T = (a b c) / (4 R)$

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

$a = \sqrt{{(5 - 3)}^{2} + {(8 - 2)}^{2}} = \sqrt{40} = 6.3246$ $a = sqrt((5-3)^2 + (8-2)^2) = sqrt 40 = 6.3246$

$b = \sqrt{{(5 - 9)}^{2} + {(8 - 4)}^{2}} = \sqrt{32} = 5.6569$ $b = sqrt((5-9)^2 + (8-4)^2) = sqrt 32 = 5.6569$

$c = \sqrt{{(9 - 3)}^{2} + {(2 - 2)}^{2}} = \sqrt{40} = 6.3246$ $c = sqrt((9-3)^2 + (2-2)^2) = sqrt 40 = 6.3246$

$Semi perimeter of the triangle s = \frac{a + b + c}{2} = 9.153$ $"Semi perimeter of the triangle " s = (a + b + c ) / 2 = 9.153$

$A_{T} = \sqrt{s} (s - a) (s - b) (s - c))$ $A_T = sqrt s (s-a) (s-b) (s - c))$

$A_{T} = \sqrt{9.153 (9.153 - 6.3246) (9.153 - 5.6569) (9.153 - (6.3246)) = 16}$ $A_T = sqrt(9.153 (9.153 - 6.3246) (9.153 - 5.6569) (9.153 - (6.3246)) = 16$

$R = \frac{a b c}{4 \cdot A_{T}} = \frac{\sqrt{40} \cdot \sqrt{32} \cdot \sqrt{40}}{4 \cdot 16} = 3.5355$ $R = (a b c ) / (4 * A_T) = (sqrt40 * sqrt32* sqrt40) / (4 * 16) = 3.5355$

$Area of Circum circle A_{R} = π R^{2} = π \cdot {3.5355}^{2} = 39.27 sq units$ $color(orange)("Area of Circum circle " A_R = pi R^2 = pi * 3.5355^2 = 39.27 " sq units"$

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

1 Answer

Explanation:

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

1 Answer

Explanation:

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