Stage: 4 Challenge Level: 
As shown in the diagram, two semi-circles (each of radius $1/2$) touch each other, and a semi-circle of radius 1 touches both of them. Find the radius of the circle which touches all three semi-circles, and find a 3-4-5 triangle in the diagram.
Creating expressions/formulae. Long problems. Pythagoras' theorem. Other equations. Manipulating algebraic expressions/formulae. Stage 5 needs dealing with. Right angled triangles. Circle theorems. Circles. Mathematical reasoning & proof.
Published October 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