MathDB

3

Part of 2008 Oral Moscow Geometry Olympiad

Problems(2)

angle chasing in a regular hexagon, 45^o given

Source: 2008 Oral Moscow Geometry Olympiad grades 8-9 p3

10/13/2020
In the regular hexagon ABCDEFABCDEF on the line AFAF, the point XX is taken so that the angle XCDXCD is 45o45^o. Find the angle ∠FXE\angle FXE.
(Kiev Olympiad)
geometryangleshexagon
is it parallelogram? midpoints, equal segments

Source: 2008 Oral Moscow Geometry Olympiad grades 10-11 p3

10/14/2020
Given a quadrilateral ABCDABCD. A′,B′,C′A ', B', C' and D′D' are the midpoints of the sides BC,CB,BABC, CB, BA and ABAB, respectively. It is known that AA′=CC′AA'= CC', BB′=DD′BB'= DD'. Is it true that ABCDABCD is a parallelogram?
(M. Volchkevich)
geometryparallelogrammidpointsequal segments