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 $r = A_t / s = 0.5025 / 6.4087 = 0.0793$

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