Chapter 10.1, Problem 5PSA

To determine

$\text{Distance of }\overline{\text{AB}}\text{ to P}\text{.}$

Answer to Problem 5PSA

8mm

Explanation of Solution

Given information :

  $\text{Chord }\overline{\text{AB}}\text{ measures 12 mm and radius is 10 mm}\text{.}$

Calculation:

  $\begin{array}{l}\text{Radius PA = 10 mm, Chord, AB = 12 mm}\\ \text{PO}\perp AB,PO\text{ bisects AB}\\ AO=6m,OB=6mm\\ In\Delta POA,\text{ using Pythagoras theorem,}\\ P{A}^2=O{P}^2+O{A}^2\\ {(10)}^2=O{P}^2+{(6)}^{2}O{P}^2={10}^2-6^2=64\\ OP=\text{8 mm, distance of }\stackrel{⌢}{\text{AB}}\text{ from P}\text{.}\end{array}$