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Just Touching

Three semi-circles have a common diameter, each touches the other two and two lie inside the biggest one. What is the radius of the circle that touches all three semi-circles?

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Pair Squares

Stage: 5 Challenge Level: Challenge Level:1

The numbers $2$, $34$ and $47$ are such that the sum of any pair of these numbers is a perfect square. Find a method for choosing three square numbers and from them finding a corresponding set of three integers with this property and give some examples.

The integers $-208$, $224$, $352$ and $737$ also have the property that the sum of any pair of these numbers is a perfect square. Find other sets of four integers with this property.