A triangle has corners at $(3, 4)$ $(3 , 4 )$ , $(5, 6)$ $(5 ,6 )$ , and $(2, 1)$ $(2 ,1 )$ . What is the radius of the triangle's inscribed circle?

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Answer 1 · 2017-06-23T08:45:46

The radius is $= 0.34$ $=0.34$

The area of the triangle is

$A=1/2|(x_1,y_1,1),(x_2,y_2,1),(x_3,y_3,1)|$

$A=1/2|(3,4,1),(5,6,1),(2,1,1)|$

$=1/2(3*|(6,1),(1,1)|-4*|(5,1),(2,1)|+1*|(5,6),(2,1)|)$

$=1/2(3(6-1)-4(5-2)+1(5-12))$

$=1/2(15-12-7)$

$=1/2|-4|=2$

The length of the sides of the triangle are

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

$b=sqrt((5-2)^2+(6-1)^2)=sqrt34$

$c=sqrt((3-2)^2+(4-1)^2)=sqrt10$

Let the radius of the incircle be $=r$

Then,

The area of the circle is

$A=1/2r(a+b+c)$

The radius of the incircle is

$r=(2a)/(a+b+c)$

$=(2*2)/(sqrt8+sqrt34+sqrt10)$

$=0.34$

A triangle has corners at (3 , 4 )(3,4)(3 , 4 ), (5 ,6 )(5,6)(5 ,6 ), and (2 ,1 )(2,1)(2 ,1 ). What is the radius of the triangle's inscribed circle?