Stage: 5 Challenge Level: 
Think about angle $APB$.
You might like to use dynamic geometry software to help with this problem. You can download geogebra for free from geogebra.org. We have pre-drawn a diagram if this is useful to you.
Mathematical reasoning & proof. Inequality/inequalities. Circle theorems. Summation of series. Manipulating algebraic expressions/formulae. epsilons. Making and proving conjectures. Stage 5 - Reviewed 2012. alphas. Dynamic geometry.
Published March 1999.
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email: nrich@damtp.cam.ac.uk