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Rectangle triangle problem

Submitted by plusadmin on 1 September, 1997
September 1997

You are given a rectangle OABC from which you remove three right-angled triangles leaving a fourth triangle OPQ as shown in the diagram below.

Triangle in rectangle

How must you position the points P and Q so that the area of each of the three removed triangles is the same? That is, what are the ratios AP:PB and CQ:QB?

Solution

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