MathDB

5

Part of 2007 Ukraine Team Selection Test

Problems(1)

some constructions with altitudes and parallel lines

Source: Ukrainian TST 2007 problem 5

9/19/2007
AA3 AA_{3} and BB3 BB_{3} are altitudes of acute-angled △ABC \triangle ABC. Points A1 A_{1} and B1 B_{1} are second points of intersection lines AA3 AA_{3} and BB3 BB_{3} with circumcircle of △ABC \triangle ABC respectively. A2 A_{2} and B2 B_{2} are points on BC BC and AC AC respectively. A1A2∥AC A_{1}A_{2}\parallel AC, B1B2∥BC B_{1}B_{2}\parallel BC. Point M M is midpoint of A2B2 A_{2}B_{2}. \angle BCA \equal{} x. Find ∠A3MB3 \angle A_{3}MB_{3}.
geometrycircumcircleparallelogramgeometric transformationreflectionEulersymmetry