Putnam 1940 A2

Let $A,B$ be two fixed points on the curve $y=f(x)$ , $f$ is continuous with continuous derivative and the arc $\widehat{AB}$ is concave to the chord $AB$ . If $P$ is a point on the arc $\widehat{AB}$ for which $AP+PB$ is maximal, prove that $PA$ and $PB$ are equally inclined to the tangent to the curve $y=f(x)$ at $P$ .