Chapter 10, Problem 4RP

a)

To determine

To find : The Radius of circle

Answer to Problem 4RP

Radius = $13$ unit

Explanation of Solution

Given Information :

We know that, OP = $5$ and PQ = $12$

  

Formula Used:

Pythagoras Theorem

(hypotenuse)2 = (Perpendicular)2 + (Base)2

Calculation :

  $\begin{array}{l}{(OP)}^2+{(PQ)}^2={(OQ)}^2{5}^2+{12}^2={(OQ)}^2\\ 25+144={(OQ)2}^{}\\ \Rightarrow OQ=\sqrt{169}\\ \Rightarrow OQ=13\text{ unit}\end{array}$

So, Radius = $13$ unit

b)

To determine

To find : The Radius of circle

Answer to Problem 4RP

Radius = $8.5$

Explanation of Solution

Given Information :

  

We know that, the length of two sides of the triangle is 15 units and 8 units

Formula Used:

Pythagoras Theorem

(hypotenuse) 2 = (perpendicular)2 + (base)2

Calculation :

  $\begin{array}{l}{8}^2+{15}^2=P{Q}^2\\ \Rightarrow P{Q}^2=64+225\\ \Rightarrow PQ=\sqrt{289}\\ \Rightarrow PQ=17\text{ units}\end{array}$

Radius = $\frac{1}{2}\times 17=8.5$ unit

c)

To determine

To find : Radius of circle

Answer to Problem 4RP

Radius = $7$ unit

Explanation of Solution

Given Information :

  

Formula Used:

Pythagoras Theorem

(hypotenuse) 2 = (perpendicular)2 + (base)2

Calculation :

Radius of a circle is $\perp$ to the tangent to a circle.

  $\begin{array}{l}P{Q}^2{24}^2={25}^2\\ P{Q}^2={25}^2-{24}^2\\ \Rightarrow PQ=7\end{array}$

So, Radius = $7$ unit

Conclusion:

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