A triangle has corners at #(8 , 6 )#, #(4 ,3 )#, and #(1 ,4 )#. What is the radius of the triangle's inscribed circle?

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Answer 1 · 2018-07-29T12:43:03

#color(green)("Radius of in-circle "= r = A_t / s = 6.5 / 7.7212 ~~ 0.8418#

#A(8, 6), B(4, 3), C(1, 4)#

#c = sqrt((8-4)^2 + (6-3)^2) ~~ 5#

#a= sqrt ((4-1)^2 + (3-4)^2) ~~ sqrt 10#

#b = sqrt((1-8)^2 + (4-6)^2) ~~ sqrt 53#

Semi perimeter #s = (a + b + c)/2 #

#s = (5 + sqrt 10 + sqrt 53 ) / 2 = 7.7212#

Area of triangle #A_t = sqrt(s (s-a) (s-b) (s-c)), " using Heron's formula"#

#A_t = sqrt(7.7212 (7.7212- 5) (7.7212-sqrt 10) (7.7212-sqrt 53)) ~~ 6.5#

#color(green)("Radius of in-circle "= r = A_t / s = 6.5 / 7.7212 ~~ 0.8418#