A triangle has corners at $(8 , 6 )$ , $(4 ,3 )$ , and $(1 ,4 )$ . What is the radius of the triangle's inscribed circle?

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Answer 1 · 2018-07-29T12:43:03

$color(green)("Radius of in-circle "= r = A_t / s = 6.5 / 7.7212 ~~ 0.8418$

$A(8, 6), B(4, 3), C(1, 4)$

$c = sqrt((8-4)^2 + (6-3)^2) ~~ 5$

$a= sqrt ((4-1)^2 + (3-4)^2) ~~ sqrt 10$

$b = sqrt((1-8)^2 + (4-6)^2) ~~ sqrt 53$

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

$s = (5 + sqrt 10 + sqrt 53 ) / 2 = 7.7212$

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

$A_t = sqrt(7.7212 (7.7212- 5) (7.7212-sqrt 10) (7.7212-sqrt 53)) ~~ 6.5$

$color(green)("Radius of in-circle "= r = A_t / s = 6.5 / 7.7212 ~~ 0.8418$

A triangle has corners at (8 , 6 )(8 , 6 ), (4 ,3 )(4 ,3 ), and (1 ,4 )(1 ,4 ). What is the radius of the triangle's inscribed circle?