1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Circle property

  1. Nov 29, 2008 #1
    1. The problem statement, all variables and given/known data
    There are two circles of equal radii. I have to prove that the mid point of the line joining their centres is the only point through which if several arbitrary lines are drawn, equal areas enclosed by the circles will fall on either side of the line.

    I cannot think of a way to proceed. I have observed the situation by drawing out equal cirlces and testing the conditions. They seem as obvious as the result of 2+2, but equally difficult to prove.
    Please help .
  2. jcsd
  3. Nov 29, 2008 #2


    User Avatar
    Science Advisor
    Homework Helper

    Pick a point that is NOT the midpoint. Can you see a way to construct a line through it that does NOT cut the circles generating equal areas? Hint: you may want to consider some special cases. Suppose the point is inside one of the circles? Suppose it's in neither? In the latter case case can you show that if you draw the two lines tangent to one circle that they aren't also tangent to the other? Then think about rotating the line 'a little'.
  4. Nov 30, 2008 #3
    I just need a formal proof that would be accepted in an exam. I cannot go on with special cases. Thanks for the help though!
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Circle property
  1. Points on a circle (Replies: 3)

  2. Tangent to a circle (Replies: 3)