MathDB

2

Part of 2003 APMO

Problems(1)

Constant = m_1+m_2

Source: APMO 2003

3/5/2006
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.
geometryperimetercircumcircletrigonometrygeometric transformationrotationangle bisector