MathDB
Putnam 1997 A1

Source:

May 30, 2014
Putnamgeometryrectanglegeometric transformationreflectioncircumcircleanalytic geometry

Problem Statement

A rectangle, HOMFHOMF, has sides HO=11HO=11 and OM=5OM=5. A triangle ΔABC\Delta ABC has HH as orthocentre, OO as circumcentre, MM be the midpoint of BCBC, FF is the feet of altitude from AA. What is the length of BCBC ?
[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("FF", F, SW); label("HH", H, NW); label("MM", M, SE); label("OO", O, NE); [/asy]