Can anyone explain this simple geometry problem to me?

Question

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/geoe.jpg/

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?

Tom · Accepted Answer

we can use the fact that in a circumscribed quadrilateral opposite angles are supplements:

so <ADC = 180 - <ABC = 180 - 60 = 120⁰

AB = AC for equilateral ∆ABC and
using ∆ADC and cosine rule we get:

AC² = AD² + DC² -2(AD)(DC)cos(<ADC)
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

rudkin · Answer

Collinear ability that they lie on one single line like of a,b,c are on an identical line then they're collinear and if enable's says c is someplace else then the standards at the instant are not collinear reason they don't seem to be on an identical line. Coplanar is whilst the standards are on an identical airplane. occasion enable's say b and c are on the airplane and a is out of the airplane then basically b and c are coplanar reason they the two are on an identical airplane. in the event that they have been to assert a and b are coplanar it would not be genuine bcuz a us not the the airplane. Get it? If u choose greater help basically digital mail me :)

Can anyone explain this simple geometry problem to me?

2 Answers