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

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Answer 1 · 2018-06-21T05:36:25

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

#"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"#