Subcontests
(6)square interior to a square, 5 equal incircles, 4 right triangles
In the figure, [ABCD] is a square of side 1. The points E,F,G and H are such that [AFB],[BGC],[CHD] and [DEA] are right-angled triangles. Knowing that the circles inscribed in each of these triangles and the circle inscribed in the square [EFGH] has all the same radius, what is the measure of the radius of the circles?
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