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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