MathDB
Points P which maximize <OPX - [Canada MO 1977]

Source:

September 29, 2011
rotation

Problem Statement

Let OO be the centre of a circle and AA a fixed interior point of the circle different from OO. Determine all points PP on the circumference of the circle such that the angle OPAOPA is a maximum.
[asy] import graph;
unitsize(2 cm);
pair A, O, P;
A = (0.5,0.2); O = (0,0); P = dir(80);
draw(Circle(O,1)); draw(O--A--P--cycle);
label("AA", A, E); label("OO", O, S); label("PP", P, N); [/asy]