A triangle has corners at #(4 , 5 )#, #(8 ,2 )#, and #(1 ,7 )#. What is the radius of the triangle's inscribed circle?

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Answer 1 · 2018-06-27T02:05:40

#color(indigo)("Radus of inscribed circle " = r = A_t / s = 0.0647 " units"#

![http://mathibayon.blogspot.com/2015/01/ derivation-of-formula-for-radius-of-incircle.html

#"Given " A (4,5), B (8,2), C(1,7)#

#c = sqrt ((8-4)^2 + (2-5)^2) = 5#

#b = sqrt ((1-4)^2 + (7-5)^2) = sqrt13 = 3.61#

#a = sqrt ((8-1)^2 + (2-7)^2) = sqrt74 = 8.602#

#s = (a + b + c) / 2 = (5 + sqrt13 + sqrt74) / 2 = 8.604#

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

#A_t = sqrt(8.604 (8.604 - 5) (8.604 - sqrt13) (8.604 - sqrt74)) = 0.5565#

#color(indigo)("Radus of inscribed circle " = r = A_t / s = 0.5565 / 8.604 = 0.0647#