# A triangle has corners at #(3 , 2 )#, #(6 ,7 )#, and #(5 ,8 )#. What is the radius of the triangle's inscribed circle?

##### 1 Answer

#### Answer

#### Answer:

#### Explanation

#### Explanation:

#### Answer:

The radius of the circle is 0.581

#### Explanation:

We determine the coordinates of the center of inscribed circle by investigation of the intersection of the angular bisectors.

Let,

Angular bisector atA:

Slope of line AB is

Slope of line AB is

Let the slope of the bisector be m

Cross multiplying

Dividing by 14

Equation of the bisector through A(3,2) is

Simplifying

Angular bisector atB:

A-=(3,2)

B-=(6,7)

C-=(5,8)

Slope of line AB is

Slope of line BC is

Let the slope of the bisector be m

Cross multiplying

Dividing by 2

Equation of the bisector through B(6,7) is

Simplifying

The lines

Equating rhs

Verified

The coordinates of the centre of incircle is

Slope of line AB

Point A is

Equation of the line AB is

Center is

Tangent is

The distance from O to the line AB is

given by

The radius of the circle is 0.581

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