In a new series of posts, I’m going to be selecting nice questions from archive exam papers, posting them, then posting possible solutions in the follow-up posts… which will contain a new question.

So here’s the first one, taken form an O-Level maths paper in 1963:

Can you solve it?

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It’s all about medians and ratios of lengths of line segments on the same or on parallel lines. This means that a transformational approach using shear and stretch, which do not affect such ratios, can turn the parallelogram into a square. I love these “sort the sheep from the goats” problems.

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