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Crossed Ladders Theorem


CrossedLaddersTheorem

In the above figure, let E be the intersection of AD and BC and specify that AB∥EF∥CD. Then

 1/(AB)+1/(CD)=1/(EF).
CrossedLaddersTheoremExt

A beautiful related theorem due to H. Stengel can be stated as follows. In the above figure, let E lie on the side AB and D lie on the side BC. Now let EC intersect the line AD at a point F, and construct points G, H, I, and J so that EI∥DH∥FJ∥BG. Then

 1/(EI)+1/(DH)=1/(FJ)+1/(BG).

See also

Crossed Ladders Problem

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Cite this as:

Weisstein, Eric W. "Crossed Ladders Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CrossedLaddersTheorem.html

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