A triangle has corners at (2 , 6 ), (8 ,2 ), and (1 ,3 ). What is the radius of the triangle's inscribed circle?

1 Answer
sankarankalyanam
Jun 21, 2018

color(orange)("Radius of incircle " r = A_t / s = 10.99 / 8.72 = 1.26 " 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(2,6), B(8,2), C(1,3)

a = sqrt((8-1)^2 + (2-3)^2) = 7.07

b = sqrt((1-2)^2 + (3-6)^2) = 3.16

c = sqrt((2-8)^2 + (6-2)^2) = 7.21

"Semi-perimeter " s = (a + b + c) / 2 = (7.07 + 3.16 + 7.21) / 2 = 8.72

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

A_t = sqrt(8.72 (8.72-7.07) (8.72 - 3.16) (8.72 - 7.21)) = 10.99

color(orange)("Radius of incircle " r = A_t / s = 10.99 / 8.72 = 1.26 " units"

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