Chapter 10, Problem 12RP

To determine

To find : The Radius of circle .

Answer to Problem 12RP

Radius $4.25$ units.

Explanation of Solution

Given information :

A parallelogram with sides $4$ and $7.5$ inscribed in a circle.

Formula Used:

Theorem : The radius of the circle containing all the vertices of the quadrilateral.

  $R=\frac{1}{4}\frac{\sqrt{(ab+cd)(ac+bd)(ad+bc)}}{\sqrt{(s-a)(s-b)(s-c)(s-d)}}$

Where $S=\frac{a+b+c+d}{2}$

Calculation :

  $\begin{array}{l}S=\frac{4+7.5+4+7.5}{2}=11.5\\ R=\frac{1}{4}\frac{\sqrt{(4\times 7.5+4\times 7.5)(4\times 4+7.5\times 7.5)(4\times 7.5+7.5\times 4)}}{\sqrt{(11.5-4)(11.5-7.5)(11.5-4)(11.5-7.5)}}\end{array}$

  $\therefore$ Radius of the circle = $4.25$ units