IB Geometry and Trigonometry Problem 009

The figure below shows a circle with centre \(O\) and radius \(8\,cm\).

The figure is not to scale.

image essential to understanding the question

Points \(A\), \(B\), \(C\), \(D\), \(E\), \(F\) are on the circle, and \(AF\) is a diameter. The length of arc \(ABC\) is \(6\,cm\).

  1. Find the measure of angle \(\angle\,AOC\).
  2. Hence, find the area of the shaded region.
  3. The area of sector \(OCDE\) is \(45\,cm^2\). Find the measure of angle \(\angle\,COE\).
  4. Find \(EF\).
Published by Annie Bernatchez in «Geometry and Trigonometry». Key Words: IB, question