Prove the shortest-path property, by considering the two paths f1pf2 and f1p f2, where f2 is the reflection of the point f2 in the line l. thus to prove that the lines f1p and f2p make equal angles wi

Prove the shortest-path property, by considering the two paths f1pf2 and f1p f2, where f2 is the reflection of the point f2 in the line l. thus to prove that the lines f1p and f2p make equal angles with the tangent, it is enough to show that f1pf2 is shorter than f1p f2 for any other point p on the tangent at p.