Stage: 4 Challenge Level: 
Prove that the shaded area of the semicircle is equal to the area of the inner circle.
What percentage of the sector OAB is taken up with the inner circle?
What happens if angle AOB is less than 90° or between 90 and 180 degrees?
Arcs, sectors and segments. Inequality/inequalities. Mixed trig ratios. Stage 5 - Reviewed 2012. Percentages. Manipulating algebraic expressions/formulae. Circles. Mathematical reasoning & proof. Number theory. Pythagoras' theorem.
Published March 1999.
Copyright © 2007. University of Cambridge. All rights reserved.
NRICH is part of the family of activities in the Millennium Mathematics Project, which also includes the Plus and Motivate sites.
email: nrich@damtp.cam.ac.uk