Chapter 10, Problem 8RP

a)

To determine

To find : Radius of $\odot A$ .

Answer to Problem 8RP

Radius = $4$ units

Explanation of Solution

Given Information:

We know that, AB = $7$ , BC = $10$ and CA = $11$

  

Calculation:

Let radius of circle A be $\text{x}$ . That of B by 'y' and of C be 'z'.

  $AB=\text{x}+\text{y}=7$     …(1)

  $BC=\text{y}+\text{z}=10$     …(2)

  $CA=\text{z}+\text{x}=11$     …(3)

Adding (1), (2) and (3), we get

  $2(\text{x}+\text{y}+\text{z})=28$     ….(4)

  $\Rightarrow x+y+z=14$

Solving equation (1), (2), (3) and (4), we get

  $x=4,y=3,z=7$

b)

To determine

To find : The largest circle of the three.

Answer to Problem 8RP

Circle with centre C.

Explanation of Solution

Given Information :

AB = $7$ , BC = $10$ and CA = $11$

Calculation :

Largest circle is the circle with centre C where radius = $z$ = $7$ units.