Abstract

An Intriguing Geometry Problem

Let ABC be an isosceles triangle (AB=AC). Angle BAC equals 20 degrees. Point D, such that angle DBC equals 60 degrees, is on side AC. Point E is on side AB such that angle ECB equals 50 degrees. Find, with proof, the measure of angle EDB. You should try to solve the problem before you come to the circle. Many solutions to the problem will be given which will review most of the theorems of first year geometry and most of the theorems of first year trigonometry. (It might be a good idea to review them ahead of time.) You will have a chance to show your proof if you find one that is different from those presented. We will also look at some variants of the problem and its history in the literature.