Why (AE)(CE)=(BE)(DE)?

If two chords intersect inside a circle, then the product of the two segments of one chord is equal to the product of the two segments of the other chord.
The given circle contains 2 chords, AC and BD. They intersect at a point E, and the following line segments are formed: AE, CE, BE, DE. Then (AE)(CE)=(BE)(DE).
In this video we show why (AE)(CE)=(BE)(DE). For this we use the definitions of inscribed angles and similar triangles.