MathDB

collinear wanted, regular hexagon

Source: 2023 Austrian Mathematical Olympiad , Junior Regional Competition , Problem 2

March 26, 2024

geometrycollinearhexagon

Problem Statement

Let

ABCDEF

be a regular hexagon with sidelength s. The points

P

and

Q

are on the diagonals

BD

and

DF

, respectively, such that

BP = DQ = s

. Prove that the three points

C

P

and

Q

are on a line.
(Walther Janous)