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Trigonometry/The Eyeball Theorem

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The Eyeball Theorem is as follows:

Take any two circles, with centres A and B, such that A is outside the second circle and B outside the first one. Let the tangents from A to the second circle cut the first circle at C and D, and the tangents from B to the first circle cut the second circle at E and F. Then the lines CD and EF are parallel and of equal length.

[needs diagram]