MathDB

some constructions with altitudes and parallel lines

Source: Ukrainian TST 2007 problem 5

September 19, 2007

geometrycircumcircleparallelogramgeometric transformationreflectionEulersymmetry

Problem Statement

AA_{3}

and

BB_{3}

are altitudes of acute-angled

\triangle ABC

. Points

A_{1}

and

B_{1}

are second points of intersection lines

AA_{3}

and

BB_{3}

with circumcircle of

\triangle ABC

respectively.

A_{2}

and

B_{2}

are points on

BC

and

AC

respectively.

A_{1}A_{2}\parallel AC

B_{1}B_{2}\parallel BC

. Point

M

is midpoint of

A_{2}B_{2}

. \angle BCA \equal{} x. Find

\angle A_{3}MB_{3}