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Say a circle of radius R1 and another circle of radius R2 intersect each other at two points. Then, what would be the ratio in which the line that joins the intersection points divide the line joining the centre? I need to know this for a high school physics problem. EDIT: If required, consider that the distance b/w the centres is given.

EDIT 2: The reason I'm not directly asking the physics problem is that this sub-problem is interesting in itself and something that I would like to know regardless. If someone needs to know the physics problem:

A mass 'm' is attached to two ideal ropes of of length L1 and L2, whose other ends are attached two a wall above, D distance apart. Calculate the tension in each rope.

zombiesauce
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  • Draw a picture. You will notice that you can make a triangle from joining the centres of the triangles, and the intersection point. You know the side lengths (they are $R_1$, $R_2$ and the distance between the origins), and now you only need to figure out the height of this triangle. The height of the triangle is equal to half of the distance between the intersection points. Easy peasy ... – Matti P. Nov 30 '20 at 08:17
  • "You can make a triangle from joining the centres of the triangles", please clarify which triangles you're talking about – zombiesauce Nov 30 '20 at 08:21
  • Well, there are only four interesting points: The two centres of the circles, and the two intersections. So take one of the intersections and two centres; draw lines between these points and voila, you have a triangle. Due to symmetry, it doesn't matter which of the two intersection points you choose. – Matti P. Nov 30 '20 at 08:23

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