# 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 $$\dfrac {a\sqrt{c}}{b}$$, where $$a, b$$ are coprime positive integers, and $$c$$ is a square-free positive integer, find $$a+b+c$$.

Bonus:

• Generalise this for any right triangle.

• Generalise this for any triangle.

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