Chapter 10, Problem 13RP

To determine

To find : The Length of RQ.

Answer to Problem 13RP

RQ = $5.54$ units

Explanation of Solution

Given information :

We know that, TP = $8$ , PQ = $6$

  

Formula Used:

If a secant and a tangent of a circle are drawn from an external point then the product of the lengths of the secant and its external segment equals the square of the length of the tangent segment.

Calculation :

So, RQ × RP = TP²

RQ (RQ + QP) = TP²

RQ² + RQ × $6$ = $8^2$

  $\begin{array}{l}\Rightarrow \text{RQ}=\frac{-6\pm \sqrt{6^2+4\times 64}}{2}=\frac{-6\pm \sqrt{292}}{2}\\ \Rightarrow \text{RQ}=-3\pm \sqrt{73}\\ \therefore \text{RQ}=-3+8.54=5.54\text{ units, RQ}\ne -3-8.54\end{array}$

Hence, length of RQ = $5.54$ units.