# Help on chords in two combined circles

1. Dec 16, 2005

### byronsakic

Hello,
i am having difficulty on a question involving chords i believe.

what i have so far is:
the length of CA is 17. therefore the length of CB is also 17 due to the fact that it is the radius of the first circle.
the length of AD is 10. Therefore BD is also 10 because it is the radius of the circle.
i can prove that AB is perpendicular to CD and forms a right angle since CD passes through the the centres of the circles, therefore it is a perpendicular bisector of the chord AB.
if you let the mid point between AB be M. you could solve for AM and BM using pythagoreom thoerem, however i would need CM and MD which i do not know how to find or at least cannot think of.
I could use cosine law, however i do not have any angles given.
can anyone help me proceed with this question in finding AB?
thanks
byron

2. Dec 16, 2005

### AKG

You can use the cosine law because you do know some angles, in particular, when you said:

i can prove that AB is perpendicular to CD and forms a right angle since CD passes through the the centres of the circles, therefore it is a perpendicular bisector of the chord AB.

Hint: You'll use the cosine law, but it will look like you're using a famous theorem, because this theorem is really just a particular case of the cosine law.

3. Dec 16, 2005

### Tide

Just split CD into two parts: x and 21 - x then use Pythagoras to find x from which AB/2 follows.

4. Dec 16, 2005

### byronsakic

thank you very much i got it :D