applying ceva's theorem

Hi, If anyone can help, I am having difficulty applying ceva's
theorem. For example,

From: http://www.cut-the-knot.org/Generalization/ceva.shtml


Corollary 3 (orthocenter)


In a triangle, altitudes intersect at a single point.

Proof

Indeed, right-angled triangles ACD and BCE are similar. Therefore CE/
DC = BE/AD. In an analogous manner, AF/EA = CF/BE and BD/FB = AD/CF.
Now


AF/FB · BD/DC · CE/EA = CE/DC · AF/EA · BD/FB
= BE/AD · CF/BE · AD/CF
= 1.

-------

I know how to get the similar triangles, and set up the ratios. I
just don't see how they get AF/FB · BD/DC · CE/EA = CE/DC · AF/EA · BD/
FB
I just can't see this from the ratios.

Any help is appreciated.

Thanks

.

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