USAMO 2011 Problem 5 Day 2 Let PPP be a given point inside quadrilateral ABCDABCDABCD . Points Q1Q_1Q1 and Q2Q_2Q2 are located within ABCDABCDABCD such that ∠Q1BC=∠ABP,∠Q1CB=∠DCP,∠Q2AD=∠BAP,∠Q2DA=∠CDP.\angle Q_1BC=\angle ABP, \angle Q_1CB=\angle DCP, \angle Q_2AD=\angle BAP, \angle Q_2DA=\angle CDP.∠Q1BC=∠ABP,∠Q1CB=∠DCP,∠Q2AD=∠BAP,∠Q2DA=∠CDP. Prove that Q1Q2‾∥AB‾\overline{Q_1Q_2}\parallel\overline{AB}Q1Q2∥AB if and only if Q1Q2‾∥CD‾\overline{Q_1Q_2}\parallel\overline{CD}Q1Q2∥CD . Dataset text AI-MO AoPS. Quoted with source. Solutions No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label. Add a solution PreviousProblem 4 NextProblem 6 Locator usamo/2011/p5 · Tag BCSJA1CAY5 · Edit this page on GitHub · Keys: j next, k previous