Putnam 1997 A1
Source:
May 30, 2014
Putnamgeometryrectanglegeometric transformationreflectioncircumcircleanalytic geometry
Problem Statement
A rectangle, , has sides and . A triangle has as orthocentre, as circumcentre, be the midpoint of , is the feet of altitude from . What is the length of ?[asy]
unitsize(0.3 cm);
pair F, H, M, O;
F = (0,0);
H = (0,5);
O = (11,5);
M = (11,0);
draw(H--O--M--F--cycle);
label("", F, SW);
label("", H, NW);
label("", M, SE);
label("", O, NE);
[/asy]