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

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Answer 1 · 2018-06-22T08:11:38

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

#"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"#