Length Of An Angle Bisector?

Geometry Level 4

Given a 5-12-13 right triangle, find the length of the angle bisector from the right angle to the hypotenuse. If this length can be expressed as acb\dfrac {a\sqrt{c}}{b}, where a,ba, b are coprime positive integers, and cc is a square-free positive integer, find a+b+ca+b+c.

Bonus:

  • Generalise this for any right triangle.

  • Generalise this for any triangle.

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