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Common Tangent
Age 14 to 16
ShortChallenge Level 
The diagram shows points A and B, the centres of the two circles, and C, on line BQ such that AC is parallel to PQ. Since ACQP is a rectangle, ACB is a right angled triangle. So By Pythagoras' Theorem, AC=4, which is also the length of PQ.
This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.
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