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Circles and triangles Various members continue to write in with solutions to the problem posed originally by Owen Hope and developed by Graham Orr. Charles Banks has written from Beckenhum in Kent: You published a contribution from Graeme Orr in the 17 June issue which gave a relationship that must be satisfied for the in-circle to have an integral radius, but left the question of which right-angle triangles fulfil this condition open. Some time ago I investigated right-angled triangles with integral sides, and found a way of categorising them which can be used to show that all right-angled triangles with integral sides have integral radii for their in-circles. I doubt that I am the first to do this, but not being a follower of mathematics or number theory, I have not seen it previously.