404

Part of 1985 All Soviet Union Mathematical Olympiad

Problems(1)

ASU 404 All Soviet Union MO 1985 pentagon contruction, symmetry wrt point

Source:

The convex pentagon

ABCDE

was drawn in the plane.

A_1

was symmetric to

A

with respect to

B

B_1

was symmetric to

B

with respect to

C

C_1

was symmetric to

C

with respect to

D

D_1

was symmetric to

D

with respect to

E

E_1

was symmetric to

E

with respect to

A

. How is it possible to restore the initial pentagon with the compasses and ruler, knowing

A_1,B_1,C_1,D_1,E_1

symmetrypentagongeometric constructionmidpointsgeometry