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Square in a triangle

Permanent link to this puzzle: mscroggs.co.uk/puzzles/78
Source: Maths Jam
A right-angled triangle has short sides of length \(a\) and \(b\). A square is drawn in the triangle so that two sides lie on the sides of the triangle and a corner lies on the hypotenuse.
What is the length of a side of the square?

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