Chapter 10.2, Problem 11PSB

To determine

To Find : $\text{AB and Radius of }\odot \text{O}$

Answer to Problem 11PSB

  $\text{AB = 8 units and Radius = 5 units}$

Explanation of Solution

Given information : $PB=3x-17,CD=15-x$

  

  $\begin{array}{l}AXOP=OD\\ \Rightarrow AB=CD\text{ [Equal chordx are equidixtant from centre]}\\ \Rightarrow 2PB=CD\text{ [Perpendicular from centre bisects the chord]}\\ \Rightarrow 2(3x-17)=15-x\\ \Rightarrow 6x-34=15-x\\ \Rightarrow 7x=49\\ \Rightarrow x=7\\ \Rightarrow AB=2(3\times 7-17)=2(21-17)=2\times 4=8\\ \text{Join O to B, In }\Delta \text{OPB}\\ O{A}^2=O{P}^2+P{A}^2\\ \Rightarrow O{A}^2=3^2+4^2=9+16=25\\ \Rightarrow OA=\sqrt{25}=5\text{ units}\end{array}$