Chapter 10.1, Problem 12PSB

To determine

Radius of circle

Answer to Problem 12PSB

  $15\text{ cm}$

Explanation of Solution

Given information : $\text{Chord 24 cm is 9 cm from the centre of circle}\text{.}$

  $\begin{array}{l}\text{AB is chord and OC}\perp \text{AB}\text{.}\\ \text{OC = 9 cm, OC bisect AB}\text{.}\\ \text{AC = BC}\\ \text{AC = BC = }\frac{\text{24}}{\text{2}}=12\text{cm}\\ \text{In triangle OCA,}\\ {\text{OA}}^{\text{2}}={\text{AC}}^{\text{2}}{\text{ + OC}}^{\text{2}},\text{ (Using phythagoras theorem)}\\ {\text{OA}}^{\text{2}}={12}^2+9^2=144+81=225\\ \text{OA}=15\text{ cm}\end{array}$