A triangle has corners at #(7 , 9 )#, #(3 ,7 )#, and #(4 ,8 )#. What is the radius of the triangle's inscribed circle?

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Answer 1 · 2018-02-04T09:12:44

Incenter radius #r = A_t / s = 1 / 4.5243 = color(green)(0.221)#

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Given the coordinates of the three vertices of a triangle ABC,
the coordinates of the incenter O are

Given A(7,9), B(3,7), C(4,8)

Using distance formula we can calculate a, b, c.

#a = sqrt((4-3)^2 + (8-7)^2) = 1.4142#

#b = sqrt((9-8)^2 + (7-4)^2) = 3.1623#

#c = sqrt((7-9)^2 + (3-7)^2) = 4.4721#

Semi perimeter #s = (a + b + c)/2 = (1.4142 + 3.1623 + 4.4721)/2 = 4.5243#

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

#A_t = sqrt(4.5243(4.5243-1.4142)(4.5243-3.1623)(4.5243-4.4721)) = 1#

Incenter radius #r = A_t / s = 1 / 4.5243 = color(green)(0.221)#