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Thanks in advance for reading my question. I have been thinking of this all day and I am stumped and hoping you can help.

I want to calculate the length of a line between two points on concentric circles. Please reference the drawing I provided. I want to find x. Assuming you know R1 and R2, as well as the skew angle of the line relative to the outer circle, is there a formula or way to determine the length of x?

One more thing, I am looking for a solution that does not use coordinates.

I hope you all can help!!! Thanks

B. Pourciau
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1 Answers1

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enter image description here

Referring to the above diagram, we have $$CD = R_1\sin\alpha \\ AD = R_1\cos\alpha \\ BD^2 = R_2^2-CD^2 \\ AB = AD - BD \\ \therefore AB = R_1\cos\alpha-\sqrt{R_2^2-R_1^2\sin^2\alpha}.$$ If the quantity under the radical is negative, then the line doesn’t intersect the inner circle.

amd
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