MathDB
Spain Mathematical Olympiad 2007, Problem 6

Source: 2007 Spain Mathematical Olympiad

June 15, 2017
geometrycircles

Problem Statement

Given a halfcircle of diameter AB=2RAB = 2R, consider a chord CDCD of length cc. Let EE be the intersection of ACAC with BDBD and FF the inersection of ADAD with BCBC. Prove that the segment EFEF has a constant length and direction when varying the chord CDCD about the halfcircle.
Back to ProblemsView on AoPS