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Quad in Quad

The points P, Q, R and S are the midpoints of the edges of a convex quadrilateral. What do you notice about the quadrilateral PQRS as the convex quadrilateral changes?

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Matter of Scale

Prove Pythagoras' Theorem using enlargements and scale factors.

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Triangle ABC is equilateral. D, the midpoint of BC, is the centre of the semi-circle whose radius is R which touches AB and AC, as well as a smaller circle with radius r which also touches AB and AC. What is the value of r/R?

Flower Show

Stage: 4 Short Challenge Level: Challenge Level:2 Challenge Level:2

It takes four gardeners four hours to dig four circular flower beds, each of diameter four metres.

How long will it take six gardeners to dig six circular flower beds, each of diameter six metres?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.  
This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.