Chapter 11.5, Problem 34WE

To determine

To determine the circumference of the given circle.

Answer to Problem 34WE

The circumference of circle is 31.4 cm.

Explanation of Solution

Given information :

The circle is inscribed in a rombus with diagonals 12 cm and 16 cm.

Let x be the side of rombus.

Hence we know,

  $\begin{array}{l}x=\sqrt{{\left(\frac{12}{2}\right)}^2+{\left(\frac{16}{2}\right)}^2}\\ x=\sqrt{6^2+8^2}\\ x=\sqrt{100}\\ x=10\end{array}$

Hence the side length of the rombus is 10cm.

When a circle is inscribed in a rombus then the side of rombus is equal to the diameter of the circle.

Hence the circumference of the circle is $2\pi \left(\frac{10}{2}\right)$ cm.

Hence the circumference of circle is 31.4 cm.