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I am stuck on a geometry construction and proof.

Construct a line which intersects two circles at chords of equal length.

You are given two circles (center point included) of different sizes and asked to construct a line going through the interior of both of them. The line segments made by the intersection of the line and the circles must be equal in length.

A compass and straightedge is allowed.

On your proof if your theorems are not commonly known please add a link to definition or write it out. :)

I also love khan academy vids on proofs.

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Bump I am still a bit stuck :) – Zachooz Apr 8 '14 at 3:04
@RicardoCruz Nvm I figured it out. You copy the diameter of the smaller circle as a chord of bigger circle then make the circle tangent to that chord with the center of the bigger circle as its center (basically, its in the bigger circle) Lastly you make a line through the center of the smaller circle tangent to the circle inside the bigger circle. Its a bit confusing to write it down but I hope u get it :P – Zachooz Apr 12 '14 at 21:05
The proof is simple. Two cords equidistant from the center of their circle are congruent. Both these cords are tangent to the inner circle so they are both congruent. The first chord was congruent to the diameter of the smaller circle so the other is too by transitive. – Zachooz Apr 12 '14 at 21:08
That's not the only solution. You can make a similar construction with any chord smaller than the diameter of the smaller circle. – RicardoCruz Apr 12 '14 at 21:09
@RicardoCruz How would that work? – Zachooz Apr 12 '14 at 21:10

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