How Do You Calculate Chord Lengths in Intersecting Circles?

  • Thread starter Thread starter byronsakic
  • Start date Start date
  • Tags Tags
    Circles
byronsakic
Messages
17
Reaction score
0
Hello,
i am having difficulty on a question involving chords i believe.
chords.jpg

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
 
Physics news on Phys.org
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.
 
Just split CD into two parts: x and 21 - x then use Pythagoras to find x from which AB/2 follows.
 
thank you very much i got it :D
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
Back
Top