A triangle has corners at $(4 , 5 )$ , $(3 ,2 )$ , and $(1 ,3 )$ . What is the radius of the triangle's inscribed circle?

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A triangle has corners at $(4 , 5 )$ , $(3 ,2 )$ , and $(1 ,3 )$ . What is the radius of the triangle's inscribed circle?

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Answer 1 · 2018-06-22T09:41:24

$color(cyan)("Radius of inscribed circle " r = A_t / s = 3.62/ 4.529 = 0.8 " units"$

Explanation:

![http://mathibayon.blogspot.com/2015/01/http://derivation-of-formula-for-radius-of-incircle.html](https://useruploads.socratic.org/qByQYJn5SEeAPjtKhB4j_incircle%20radius.png)

$"Incircle radius " r = A_t / s$

$A(4,5), B(3,2), C(1,3)$

$a = sqrt((3-1)^2 + (2-3)^2) = 2.236$

$b = sqrt((1-4)^2 + (3-5)^2) = 3.606$

$c = sqrt((4-3)^2 + (5-2)^2) = 3.162$

$"Semi-perimeter " s = (a + b + c) / 2 = (2.236 + 3.606 + 3.162) / 2 = 4,529$

$"A_t = sqrt(s (s-a) s-b) (s-c))$

$A_t = sqrt(4.529 (4.529-2.236) (4.529 - 3.606) (4.529 - 3.162)) = 3.62$

$color(cyan)("Radius of inscribed circle " r = A_t / s = 3.62/ 4.529 = 0.8 " units"$

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A triangle has corners at $(4 , 5 )$ , $(3 ,2 )$ , and $(1 ,3 )$ . What is the radius of the triangle's inscribed circle?

1 Answer

Explanation:

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A triangle has corners at (4 , 5 )(4 , 5 ), (3 ,2 )(3 ,2 ), and (1 ,3 )(1 ,3 ). What is the radius of the triangle's inscribed circle?

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A triangle has corners at $(4 , 5 )$ , $(3 ,2 )$ , and $(1 ,3 )$ . What is the radius of the triangle's inscribed circle?