Incircles in Right Triangles

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This Sangaku from the Iwate prefecture is undated.

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Take a right triangle. Draw the altitude from the right angle. This defines two new right triangles.

The sum of the radii of the incircles of the three triangles equals the length of the altitude.

The result is unexpected. The proof is not difficult.

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Contributed by: Claude Fabre (March 2011)
Open content licensed under CC BY-NC-SA


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