Points P which maximize <OPX - [Canada MO 1977]
Source:
September 29, 2011
rotation
Problem Statement
Let be the centre of a circle and a fixed interior point of the circle different from . Determine all points on the circumference of the circle such that the angle 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("", A, E);
label("", O, S);
label("", P, N);
[/asy]