Stage: 4 and 5 Challenge Level: 
You need one of the circle theorems here and the formula for arc
length.
Perimeters. Mathematical reasoning & proof. Circle theorems. Dynamic geometry. Arcs, sectors and segments. Circles. Making and proving conjectures. Generalising. Interactivities. Stage 5 - Reviewed 2012.
Published July 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