Show how to construct a chord $BPC$ of a given angle $A$ through a given point $P$ such that $\tfrac{1}{BP}+ \tfrac{1}{PC}$ is a maximum. [asy][asy] size(200); defaultpen(linewidth(0.7)); pair A = origin, B = (5,0), C = (4.2,3), P = waypoint(B--C,0.65); pair Bp = 1.3 * B, Cp = 1.2 * C; draw(A--B--C--A^^Bp--A--Cp); dot(P); label("$A$",A,W); label("$B$",B,S); label("$C$",C,dir(B--C)); label("$P$",P,dir(A--P)); [/asy][/asy]
Problem
Source: USAMO 1979 Problem 4-edited to proper wording
Tags: geometry, trapezoid, geometry unsolved