A triangle has corners at #(2 , 3 )#, #(1 ,5 )#, and #(6 ,7 )#. What is the radius of the triangle's inscribed circle?

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Answer 1 · 2018-07-29T12:27:15

#color(orange)("Radius of in-circle "= r = A_t / s ~~ 0.9038#

#A(2, 3), B(1, 5), C(6, 7)#

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

#a= sqrt ((1-6)^2 + (5-7)^2) ~~ sqrt 29#

#b = sqrt((6-2)^2 + (7-3)^2) ~~ sqrt 32#

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

#s = (sqrt 5 + sqrt 29 + sqrt 32 ) / 2 = 6.639#

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

#A_t = sqrt(6.639 (6.639- sqrt 5) (6.639-sqrt 29) (6.639-sqrt 32)) ~~ 6#

#color(orange)("Radius of in-circle "= r = A_t / s = 6 / 6.639 ~~ 0.9038#