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

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Answer 1 · 2018-07-29T13:13:33

In-circle radius #color(chocolate)(r = A_t / s ~~ 0.9617 “ units”#

#A(7, 9), B(3 7), C(1, 1)#

#c = sqrt((7-3)^2 + (9-7)^2) ~~ sqrt 20#

#a= sqrt ((3-1)^2 + (7-1)^2) ~~ sqrt 40#

#b = sqrt((1-7)^2 + (1-9)^2) = 10#

Semi perimeter #s = (a + b + c)/2 = (sqrt 20 + sqrt 40 + 10) / 2 = 10.3983#

Applying Heron’s formula,

#A_t = sqrt(s (s-a) (s-b) (s-c)) = sqrt(10.3983 (10.3983- sqrt 20) (10.3983-sqrt 40) (10.3983 - 10)) ~~ 10#

In-circle radius #color(chocolate)(r = A_t / s = 10 / 10.3983 ~~ 0.9617 “ units”#