A triangle has corners at $(4 , 5 )$ , $(1 ,3 )$ , and $(3 ,3 )$ . What is the radius of the triangle's inscribed circle?

Question

1580 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-29T12:50:48

$color(indigo)("Radius of in-circle "= r = A_t / s = 2 / 3.9208 ~~ 0.5101$

$A(4, 5), B(1 3), C(3, 3)$

$c = sqrt((4-1)^2 + (5-3)^2) ~~ sqrt 13$

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

$b = sqrt((3-4)^2 + (3-5)^2) ~~ sqrt 5$

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

$s = (sqrt 13 + 2 + sqrt 5 ) / 2 = 3.9208$

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

$A_t = sqrt(3.9208 (3.9208- sqrt 13) (3.9208- 2) (3.9208-sqrt 5)) ~~ 2$

$color(indigo)("Radius of in-circle "= r = A_t / s = 2 / 3.9208 ~~ 0.5101$

A triangle has corners at (4 , 5 )(4 , 5 ), (1 ,3 )(1 ,3 ), and (3 ,3 )(3 ,3 ). What is the radius of the triangle's inscribed circle?