MathDB

Equilateral triangle and an unit circle

Source: JBMO 2008 Problem 2

June 25, 2008

geometrytrigonometryangle bisectorperpendicular bisectorpower of a pointgeometry proposed

Problem Statement

The vertices

A

and

B

of an equilateral triangle

ABC

lie on a circle

k

of radius

1

, and the vertex

C

is in the interior of the circle

k

. A point

D

, different from

B

, lies on

k

so that AD\equal{}AB. The line

DC

intersects

k

for the second time at point

E

. Find the length of the line segment

CE