MathDB

3

Part of 2001 Bundeswettbewerb Mathematik

Problems(2)

Prove that triangle ABC is equilateral

Source: Germany Bundeswettbewerb Mathematik 2001, Round 2, Problem 3

1/31/2009
Let ABC ABC be a triangle. Points A′,B′,C′ A',B',C' are on the sides BC,CA,AB, BC, CA, AB, respectively such that we have \overline{A'B'} \equal{} \overline{B'C'} \equal{} \overline{C'A'} and \overline{AB'} \equal{} \overline{BC'} \equal{} \overline{CA'}. Prove that triangle ABC ABC is equilateral.
geometry unsolvedgeometry
Quadrilateral BECD and triangle ABC have the same area

Source: Germany Bundeswettbewerb Mathematik 2001, Round 1, Problem 3

2/1/2009
Let ABC ABC an acute triangle with circumcircle center O. O. The line (BO) (BO) intersects the circumcircle again in D, D, and the extension of the altitude from A A intersects the circle in E. E. Prove that the quadrilateral BECD BECD and the triangle ABC ABC have the same area.
geometrycircumcircleparallelogramtrigonometrygeometry unsolved