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Triangle

Source: Greece National Olympiad 2002 , Juniors , Problem 1.

November 18, 2005

geometrytrigonometry

Problem Statement

In the exterior of an equilateral triangle

ABC

of side

\alpha

we construct an isosceles right-angled triangle

ACD

with

\angle CAD=90^0.

The lines

DA

and

CB

meet at point

E

. (a) Find the angle

\angle DBC.

(b) Express the area of triangle

CDE

in terms of

\alpha.

(c) Find the length of

BD.

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