IIT JEE Trigonometry 2000 - Given a right triangle find the sum of the in/circumcircle radius

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In this trigonometry problem from the 2000 IIT JEE we are given a right angled triangle and asked to find the sum of the incircle and circumcircle radius in terms of the sides of the triangle. The solution is simple but you need to be aware of the reasoning path to follow.
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