SOLUTION: I'm not sure if this is too big a question but if someone could at least point me in the right direction I'd appriciate it. Place 3 circles with the same radius, r, with their cen

Question 305478: I'm not sure if this is too big a question but if someone could at least point me in the right direction I'd appriciate it.
Place 3 circles with the same radius, r, with their centers on a horizontal in such a way that the middle circle intersects the left and right circles in exactly 1 point each(like 3 coins, touching, all in a row). Draw a line from the center of the left circle that is tangent to the right circle. This line intersects the middle circle in 2 points. Find the length of the line segment connecting these 2 points in terms of r.
Ok so I have the picture fine I'm pretty sure about that. In the middle circle i tried drawing radii from the center to the points of the segment i have to find the length of, and i know it's an isosceles triangle but that doesn't help me find the length of that segment. I've also tried right triangles in different areas but nothing i have come up with has helped...once again I'd really appriciate it if someone could at least steer me in the right direction. Thanks!
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Make the origin the center of your first circle (left hand side).
The center of the middle circle is then (,) and the equation of the middle circle is then,

The tangent line also starts at (,) and has has the formula,

The tangent line is the base of a right triangle that has a hypotenuse equal to and the other side . The third side is then, by the Pythagorean theorem,

The tangent of the angle that the tangent line makes with the x-axis is then equal to opposite side, , over the adjacent side, . This is also the slope you need "m".

You can then plug that into your circle equation to find the two intersection points.

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.
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Once you have the points, you can use the distance formula to calculate the distance between the points.

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