A triangle has corners at $(5, 8)$ $(5 ,8 )$ , $(3, 9)$ $(3 ,9 )$ , and $(4, 7)$ $(4 ,7 )$ . What is the area of the triangle's circumscribed circle?

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A triangle has corners at $(5, 8)$ $(5 ,8 )$ , $(3, 9)$ $(3 ,9 )$ , and $(4, 7)$ $(4 ,7 )$ . What is the area of the triangle's circumscribed circle?

1 Answer

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Answer 1 · 2016-08-28T02:32:44

the area of the circle inscribed = 0.8160

Explanation:

the triangle is isoceles, side lengths = $\sqrt{5}, \sqrt{5} and \sqrt{2}$ $sqrt5, sqrt5 and sqrt2$
triangle area (A) = $\frac{1}{2} \times \sqrt{2} \times \frac{3}{\sqrt{2}} = \frac{3}{2}$ $1/2xxsqrt2xx3/sqrt2=3/2$
triangle perimeter (P) = $\sqrt{5} + \sqrt{5} + \sqrt{2} = 2 \sqrt{5} + \sqrt{2} = 5.8863$ $sqrt5+sqrt5+sqrt2=2sqrt5+sqrt2=5.8863$
inradius (r) = $\frac{2 A}{P}$ $(2A)/P$ = $2 \times \frac{1.5}{5.8863} = 0.50965$ $2xx1.5/5.8863=0.50965$
area of the circle = $π \times r^{2} = π \times {(0.50965)}^{2}$ $pixxr^2 = pixx(0.50965)^2$
$= 0.8160$ $=0.8160$

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A triangle has corners at $(5, 8)$ $(5 ,8 )$ , $(3, 9)$ $(3 ,9 )$ , and $(4, 7)$ $(4 ,7 )$ . What is the area of the triangle's circumscribed circle?

1 Answer

Explanation:

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A triangle has corners at (5,8)(5 ,8 ), (3,9)(3 ,9 ), and (4,7)(4 ,7 ). What is the area of the triangle's circumscribed circle?

1 Answer

Explanation:

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A triangle has corners at $(5, 8)$ $(5 ,8 )$ , $(3, 9)$ $(3 ,9 )$ , and $(4, 7)$ $(4 ,7 )$ . What is the area of the triangle's circumscribed circle?