3
Part of 2004 Bundeswettbewerb Mathematik
Problems(2)
Two congruent regular hexagons
Source: BWM 2004, 1st round, problem 3
9/3/2004
Prove that two congruent regular hexagons can be cut up into (altogether) parts such that these parts can be composed to form an equilateral triangle (without gaps or overlaps).
Triangle geometry, bisecting chords
Source: BWM 2004, 2nd round, problem 3
9/1/2004
Given two circles and which intersect at two different points and . The tangent to the circle at the point meets the circle again at the point . The tangent to the circle at the point meets the circle again at the point . Finally, let the line meet the circle in a point different from and .
Prove that the line bisects the chord .
geometryratiosimilar trianglesgeometry proposed