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

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Answer 1 · 2018-01-05T12:54:02

Radius of the triangle's inscribed circle is $1.07$ unit.

The three corners are $A (1,2) B (5,2) and C (3,5)$

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 $AB= sqrt ((1-5)^2+(2-2)^2) =4$ unit

Side $BC= sqrt ((5-3)^2+(2-5)^2) ~~3.61$ unit

Side $CA= sqrt ((3-1)^2+(5-2)^2) ~~ 3.61$ unit

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

$s= (4+3.61+3.61)/2~~ 5.61$ unit

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

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

$A_t = |1/2(-3+15+0)| = | 6.0| =6.0$ sq.unit

Incircle radius is $r_i= A_t/s = 6.0/5.61 ~~1.07$ unit

Radius of the triangle's inscribed circle is $1.07$ unit [Ans]

[Ans]

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