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A circle is inscribed into a right triangle. From the center of the circle a perpendicular is dropped on the hypotenuse, dividing the hypotenuse into two segments of length 12 and 5. What is the sum of the legs of the triangle?

 

I did draw the diagram, and connected the center of the circle to the edges, but I cannot go on from there. Could somebody help me? Thanks!

 Apr 11, 2024
 #1
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If I am not mistaken, this is the diagram to corresponding to your question. We can then find a because of the inradius formula (a+b-c)/2 so a=3.

the sides then form a pythagorean triple 8,15,17 and 8+15+17 = 40, the answer.

 Apr 11, 2024

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