MathDB
Constant = m_1+m_2

Source: APMO 2003

March 5, 2006
geometryperimetercircumcircletrigonometrygeometric transformationrotationangle bisector

Problem Statement

Suppose ABCDABCD is a square piece of cardboard with side length aa. On a plane are two parallel lines ℓ1\ell_1 and ℓ2\ell_2, which are also aa units apart. The square ABCDABCD is placed on the plane so that sides ABAB and ADAD intersect ℓ1\ell_1 at EE and FF respectively. Also, sides CBCB and CDCD intersect ℓ2\ell_2 at GG and HH respectively. Let the perimeters of △AEF\triangle AEF and △CGH\triangle CGH be m1m_1 and m2m_2 respectively. Prove that no matter how the square was placed, m1+m2m_1+m_2 remains constant.
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