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Tangent Triangle

Author:
John Golden
Topic:
Circle
Ed Southall (@solvemymaths) tweeted this nicely elegant geometry problem. Given a right triangle tangent to a circle, which is also tangent to the extended legs of the triangle, what is the radius of the circle? It really tickled me that the two legs and the radius make a solvable triple. If you know any two, the third is determined!

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