MathDB

Nice collinearity in regular pentagon

Source: Kvant Magazine No.11 2019 M2583

March 14, 2023

geometrypantagonKvant

Problem Statement

On the side

DE

and on the diagonal

BE

of the regular pentagon

ABCDE

we consider the squares

DEFG

and

BEHI

.
[*] Prove that

A,I,

and

G

are collinear. [*] Prove that on this line lies also the centre

O

of the square

BDJK