A triangle has corners at (6 , 3 ), (1 ,5 ), and (2 ,5 ). What is the radius of the triangle's inscribed circle?

1 Answer
sankarankalyanam
Jun 22, 2018

color(indigo)("Radius of incircle " r = A_t / s = 1.55 / 5.92 ~~ 0.26 " 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(6,2), B(1,5), C(2,5)

a = sqrt((1-2)^2 + (5-5)^2) = 1

b = sqrt((2-6)^2 + (5-2)^2) = 5

c = sqrt((6-1)^2 + (2-5)^2) = 5.83

"Semi-perimeter " s = (a + b + c) / 2 = (1 + 5 + 5.83) / 2 = 5.92

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

A_t = sqrt(5.92 (5.92-1) (5.92 - 5) (5.92 - 5.83)) = 1.55

color(indigo)("Radius of incircle " r = A_t / s = 1.55 / 5.92 ~~ 0.26 " units"

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