IB Geometry and Trigonometry Problem 003

The figure is not to scale.

image essential to understanding the question

The figure shows a sector of a circle with radius \(r\,cm\) and central angle \(\theta\). The perimeter of the sector is \(20\,cm\).

  1. Show that \(\theta = \frac{20 - 2r}{r}\).
  2. The area of this sector is \(25\,cm^2\). Find the value of \(r\).
Published by Annie Bernatchez in «Geometry and Trigonometry». Key Words: IB, question