Five years ago Mathilde was six times older than her daughter. After five years, Mathilde will be 10 years more than two times the age of her daughter. Find the present age of Mathilde and her daughter.
In the given figure, ^@ AB ^@ is a chord of length ^@ 11 \space cm ^@ of a circle with center ^@ O ^@ and radius ^@ 7 \space cm ^@. The tangents at ^@ A ^@ and ^@ B ^@ intersect at ^@ P ^@. What is the length of ^@ PA ^@?