A triangle has corners at #(7 , 9 )#, #(3 ,7 )#, and #(1 ,8 )#. What is the radius of the triangle's inscribed circle?

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Answer 1 · 2018-03-02T14:10:57

Radius of inscribed circle #r_i = A_t / s = 44.72 / 6.4 = color(purple)(6.99#

Steps :
1. Find the lengths of the three sides using distance formula
#d = sqrt((x2 - x1)^2 + (y2 - y1)^2)#

Find the area of the triangle using formula
#A_t = sqrt(s (s - a) (s - b) ( s - c))#

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

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#a = sqrt((3-1)^2 + (7-8)^2) = 2.24#

#b = sqrt((7-1)^2 + (9-8)^2) = 6.08#

#c = sqrt((7-3)^2 + (9-7)^2) = 4.47#

#s = (2.24 + 6.08 + 4.47) / 2 = 6.4#

#A_t = sqrt(6.4 * (6.4-2.24) ( 6.4 - 6.08) (6.4 - 4.47)) = 44.72#

#r_i = A_t / s = 44.72 / 6.4 = color(purple)(6.99#