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A theorem about running round a triangle and two applications

Published online by Cambridge University Press:  16 November 2021

Keith Austin
Keith Austin*
Affiliation:
Dept. of Pure Maths, Sheffield University
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Extract

Diana runs from A to B with speed u and then from B to C with speed v. Eric runs from A to C with speed w. They start together and finish together.

If we now draw three lines from a point O, with OP parallel to AB and of length u, OQ parallel to BC and of length v and OR parallel to AC and of length w, then we find P, Q and R are collinear.

It is not difficult to construct a proof of the theorem so that is left as an exercise for the reader.

Type
Research Article
Information
The Mathematical Gazette , Volume 75 , Issue 472 , June 1991 , pp. 137 - 140
Copyright
Copyright © The Mathematical Association 1991

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