A triangle has corners at #(4 , 5 )#, #(1 ,3 )#, and #(3 ,3 )#. What is the radius of the triangle's inscribed circle?

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Answer 1 · 2018-07-29T12:50:48

#color(indigo)("Radius of in-circle "= r = A_t / s = 2 / 3.9208 ~~ 0.5101#

#A(4, 5), B(1 3), C(3, 3)#

#c = sqrt((4-1)^2 + (5-3)^2) ~~ sqrt 13#

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

#b = sqrt((3-4)^2 + (3-5)^2) ~~ sqrt 5#

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

#s = (sqrt 13 + 2 + sqrt 5 ) / 2 = 3.9208#

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

#A_t = sqrt(3.9208 (3.9208- sqrt 13) (3.9208- 2) (3.9208-sqrt 5)) ~~ 2#

#color(indigo)("Radius of in-circle "= r = A_t / s = 2 / 3.9208 ~~ 0.5101#