Feliz 2015 a todos da lista! Alguém pode me ajudar a resover a 3a. questão da RMM 2010?
Let A_(1)A_(2)A_(3)A_(4) be a quadrilateral with no pair of parallel sides. For each i = 1, 2, 3, 4, define w_(1) to be the circle touching the quadrilateral externally, and which is tangent to the lines A_(i-1)A_(i) , A_(i)A_(i+1) and A_(i+1)A_(i+2) (indices are considered modulo 4 so A_(0) = A_(4), A_(5) = A_(1) and A_(6) = A_(2)). Let T_(i) be the point of tangency of w_(i) with the side A_(i)A_(i+1). Prove that the lines A_(1)A_(2), A_(3)A_(4) and T_(2)T_(4) are concurrent if and only if the lines A_(2)A_(3), A_(4)A_(1) and T_(1)T_(3) are concurrent. Abraços, Martins Rama. -- Esta mensagem foi verificada pelo sistema de antiv�rus e acredita-se estar livre de perigo.
