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British Mathematical Olympiad Round 1 December 2019

24th February 2020

Lydia Nottingham (Year 11) and Tom Ansell (Year 13) qualified for the British Olympiad Round 1. They had to sit a 3.5 hour mathematical paper consisting of 6 demanding questions. Full written solutions were expected. They both did brilliantly. Lydia achieved a merit and Tom scored a distinction. What an achievement for both of them. Well done!

This is one of the questions from the competition. Have a go! Of course both Lydia and Tom got full marks on this question!

Two circles S1 and S2 are tangent at P. A common tangent, not through P, touches S1 at A and S2 at B. Points C and D, on S1 and S2 respectively, are outside the triangle APB and are such that P is on the line CD. Prove that AC is perpendicular to BD.

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