A triangle has corners at $(2 , 3 )$ , $(1 ,5 )$ , and $(6 ,7 )$ . What is the radius of the triangle's inscribed circle?

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Answer 1 · 2018-07-29T12:27:15

$color(orange)("Radius of in-circle "= r = A_t / s ~~ 0.9038$

$A(2, 3), B(1, 5), C(6, 7)$

$c = sqrt((2-1)^2 + (3-5)^2) ~~ sqrt 5$

$a= sqrt ((1-6)^2 + (5-7)^2) ~~ sqrt 29$

$b = sqrt((6-2)^2 + (7-3)^2) ~~ sqrt 32$

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

$s = (sqrt 5 + sqrt 29 + sqrt 32 ) / 2 = 6.639$

Area of triangle $A_t = sqrt(s (s-a) (s-b) (s-c)), " using Heron's formula"$

$A_t = sqrt(6.639 (6.639- sqrt 5) (6.639-sqrt 29) (6.639-sqrt 32)) ~~ 6$

$color(orange)("Radius of in-circle "= r = A_t / s = 6 / 6.639 ~~ 0.9038$

A triangle has corners at (2 , 3 )(2 , 3 ), (1 ,5 )(1 ,5 ), and (6 ,7 )(6 ,7 ). What is the radius of the triangle's inscribed circle?