A triangle has corners at $(3 , 5 )$ , $(4 ,2 )$ , and $(8 ,4 )$ . What is the radius of the triangle's inscribed circle?

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Answer 1 · 2018-02-08T11:45:54

Radius of triangle's inscribed circle is $1.1$ unit.

The three corners are $A (3,5) B (4,2) and C (8,4)$

Distance between two points $(x_1,y_1) and (x_2,y_2)$ is

$D= sqrt ((x_1-x_2)^2+(y_1-y_2)^2$

Side $AB= sqrt ((3-4)^2+(5-2)^2) ~~ 3.16$ unit

Side $BC= sqrt ((4-8)^2+(2-4)^2) ~~4.47$ unit

Side $CA= sqrt ((8-3)^2+(4-5)^2) ~~ 5.1$ unit

The semi perimeter of triangle is $s=(AB+BC+CA)/2$ or

$s= (3.16+4.47+5.1)/2~~ 12.73/2~~ 6.37$ unit.

Area of Triangle is $A_t = |1/2(x1(y2−y3)+x2(y3−y1)+x3(y1−y2))|$

$A_t = |1/2(3(2−4)+4(4−5)+8(5−2))|$ or

$A_t = |1/2(-6-4+24)| = | 7.0| =7.0$ sq.unit.

Incircle radius is $r_i= A_t/s = 7.0/6.37 ~~1.1$ unit

Radius of triangle's inscribed circle is $1.1$ unit[Ans]

A triangle has corners at (3 , 5 )(3 , 5 ), (4 ,2 )(4 ,2 ), and (8 ,4 )(8 ,4 ). What is the radius of the triangle's inscribed circle?