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

1 Answer
sankarankalyanam
Jun 22, 2018

#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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