A triangle has corners at #(2 , 4 )#, #(1 ,3 )#, and #(6 ,7 )#. What is the radius of the triangle's inscribed circle?

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Answer 1 · 2018-07-22T13:56:21

Radius of the inscribed circle #color(blue)(r = 0.0793)#

#A(2,4), B(1,3), C(6,7)#

#a = sqrt((1-6)^2 + (3-7)^2) ~~ 6.4031#

#b = sqrt ((6-2)^2 + (7-4)^2) = 5#

#c = sqrt((2-1)^2 + (4-3)^2) ~~ 1.4142#

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

#s = (6.4031 + 5 + 1.4142) / 2 = 6.4087#

Area of triangle #A_t = sqrt(s (s-a) (s-b) (s-c))#

#A_t = sqrt(6.4087 (6.4087-6.4031) (6.4087-5) (6.4087-1.4142)) = 0.5025#

In-radius #r = A_t / s = 0.5025 / 6.4087 = 0.0793#