Chapter 10.1, Problem 16PSB

To determine

  $\text{Centre and radius of }\odot \text{O}\text{.}$

Answer to Problem 16PSB

  $\text{Centre (1, 9}\text{.5), radius 8}\text{.5}\text{.}$

Explanation of Solution

Given information :

  $\begin{array}{l}\overline{\text{PQ}}\text{ is a diameter of }\odot \text{O}\text{.}\\ P=(-3,17)\text{ and }Q=(5,2)\end{array}$

  $\begin{array}{l}\text{O is the mid point of PQ}\text{. Since, PQ is diameter}\text{.}\\ \text{Coordinate of O is,}\\ \left(\frac{-3+5}{2},\frac{17+2}{2}\right)=\left(\frac{2}{2},\frac{19}{2}\right)=\left(1,\frac{19}{2}\right)\\ \text{Centre O is }\left(\text{1,}\frac{\text{19}}{\text{2}}\right)=(1,9.5)\\ \text{Radisu is distance between }\left(\text{1,}\frac{\text{19}}{\text{2}}\right)\text{ and (5, 2)}\\ \text{OQ = }\sqrt{{(5-1)}^2+{\left(2-\frac{19}{2}\right)}^2}=\sqrt{16+\frac{225}{4}}=\sqrt{\frac{289}{4}}=\frac{17}{2}=8.5\\ \text{Radius is 8}\text{.5}\text{.}\end{array}$