Simple (should be!) Geometry Proof: Two tangents to a circle
I found this little proof in a book I was practicing out of. Does anyone have a proof for this? It must be so simple! Gaahh!
Let y be a circle, l and m be two nonparallel lines that are tangent to y at the points P and Q, and let A be the point of intersection of l and m. Prove that:
i) O lies on the bisector of angle(PAQ)
ii) PA = QA
iii) The line PQ is perpendicular to the line OA
I know Triangle POQ is isosceles, and OP = PQ, etc etc all the things about that triangle, but I don't know how to work the point A into the mix, nor do I know anything (I don't think) about Triangle PQA. Any help here?