000RM.dvi

11.6 Construction of a regular 17-gon 331

Project

This is a classic problem you should know if you teach geometry. While
it is not difficult to guess what the answer is, it has been quite baffling to
most people to arrive at the answer logically.

ABCis an isosceles triangle with angleA =20◦. Eand

Fare points onAC andABsuch that∠EBC =60◦and

∠FCB=50◦. Calculate∠BEF.

A

B C

E

F

60 ◦ 50 ◦

20 ◦