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

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Answer 1 · 2018-03-02T12:01:33

Radius of the Incircle is $r_i = A_t / s = 3.46 / 4.82 ~~color(green)( 0.72$

Given $A (2,6), B(4,7), C (1,3)$

To find the radius of the Incircle.

Using distance formula between B, C

$a = sqrt((4-1)^2 + (7-3)^2) ~~ 4.24$

Similarly, $b = sqrt((2-1)^2 + (6-3)^2) ~~ 3.16$

$c = sqrt((4-2)^2 + (7-6)^2) ~~ 2.24$

Semi perimeter of the triangle

$s = (a+ b + c) / 2 =(4.24 + 3.16 + 2.24)/2 = 4.82$

Area of triangle, knowing three sides
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$A_t = sqrt(s (s-a) (s - b) (s - c))$ where s is the semi perimeter.

$A_t = sqrt(4.82 * 0.58 * 1.66 * 2.58) ~~ color(brown)(3.46$

enter image source here

Inradius $r_i = A_t / s = 3.46 / 4.82 ~~color(green)( 0.72$

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