A triangle has corners at #(6 , 3 )#, #(3 ,5 )#, and #(2 ,9 )#. What is the radius of the triangle's inscribed circle?

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Answer 1 · 2018-06-21T05:22:29

#color(cyan)("Radius of incircle " r = A_t / s = 5 / 7.47 = 0.67 " units"#

#"Incircle radius " r = A_t / s#

#A(6,3), B(3,5), C(2,9)#

#a = sqrt((3-2)^2 + (5-9)^2) = sqrt17#

#b = sqrt((6-2)^2 + (3-9)^2) = sqrt52#

#c = sqrt((6-3)^2 + ( 3-5)^2) = sqrt13#

#"Semi-perimeter " s = (a + b + c) / 2 = (sqrt17 + sqrt52 + sqrt13) / 2 = 7.47#

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

#A_t = sqrt(7.47 (7.47-sqrt17) (7.47 - sqrt52) (7.47 - sqrt13)) = 5#

#color(cyan)("Radius of incircle " r = A_t / s = 5 / 7.47 = 0.67 " units"#