Trigonometry/The Eyeball Theorem

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]