Can anyone explain this simple geometry problem to me

Hi, does anybody know how to solve this geometry question? It's very simple but it's been a long time since I was in school.

diagram:
http://imageshack.us/photo/my-images/641…

ABC is an equilateral triangle whose points touch a circle.
D is a point on the circle.
length of AD is 2.
length of DC is 1.
length of BD is 3.

question:
what is the ratio of lengths DC to AB?

can anyone show me how this question is solved?

we can use the fact that in a circumscribed quadrilateral opposite angles are supplements:

so
AB = AC for equilateral ∆ABC and
using ∆ADC and cosine rule we get:

AC² = AD² + DC² -2(AD)(DC)cos( AB² = 2² + 1² - 2(2)(1)cos(120⁰)
AB² = 5 - 4(-1/2) = 7
AB = √7

DC:AB = 1:√7
or
DC/AB = 1/√7