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A circular tour of some circle theorems

Published online by Cambridge University Press:  01 August 2016

Nick Lord  and
David Wells
Nick Lord
Affiliation:
Tonbridge School, Kent TN9 1JP
David Wells
Affiliation:
19 Menelik Road, London NW2 3RJ
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Extract

The following theorem about circles (which can be traced back at least as far as Archimedes) does not seem to be widely known and may be used to “pep-up” a discussion of circle theorems.

THEOREM. Let two chords of a circle meet at P and make a fixed angle θ (radians, say) with each other. Then the sum of the (opposite) arc lengths, L + L′, is independent of the position of P inside the circle (and thus, taking P at the centre, this sum equals 2rθ, where r is the radius of the circle).

Type
Research Article
Information
The Mathematical Gazette , Volume 73 , Issue 465 , October 1989 , pp. 188 - 191
Copyright
Copyright © The Mathematical Association 1989

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