A circle touches the side BC of triangle ABC at P. Side AB and AC are produced to touch the circle at points Q and R respectively. The length of AQ is:
1
\(\frac{1}{2} (BC + CA + AB)\)
2
\(\frac{1}{3} (BC + CA + AB)\)
3
\(\frac{1}{2} (2BC + 2CA + 2AB)\)
4
\(\frac{1}{4} (BC + CA + AB)\)