A triangle has corners at (1 , 5 ), (4 ,8 ), and (9 ,7 ). What is the radius of the triangle's inscribed circle?

1 Answer
Narad T.
Jun 8, 2017

The radius of the inscribed circle is =1.02

Explanation:

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Let the radius of the inscribed circle be =r

The area of the triangle is

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

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

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

Let,

A=(4,8)

B=(1,5)

C=(9,7)

a=sqrt((9-1)^2+(7-5)^2)=sqrt(64+4)=sqrt68

b=sqrt((9-4)^2+(7-8)^2)=sqrt(25+1)=sqrt26

c=sqrt((4-1)^2+(8-5)^2)=sqrt(9+9)=sqrt18

so,

(a+b+c)=sqrt68+sqrt26+sqrt18

The area of the triangle is

A=1/2|(4,8,1),(1,5,1),(9,7,1)|

=1/2(4*|(5,1),(7,1)|-8*|(1,1),(9,1)|+1*|(1,5),(9,7)|)

=1/2((4*-2)-(8*-8)+(1*-38))

=1/2(-8+64-38)

=9

Therefore,

r=(2*9)/(sqrt68+sqrt26+sqrt18)=1.02

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