The
"intersecting chord segment product property" a.k.a. the "intersecting chords
theorem" says the products of the two segments of chords cut by their point of
intersection are equal. That is,

(BP)(CP) = (DP)(AP)

To see why this is true, note that triangles ABP and CDP are similar.
From the Central Angle
Theorem, we see that angles A and C are the same, and for the same reason,
angles B and D are the same. The angle P of each triangle is the same by
Vertical Angles, so the triangles are similar. Setting corresponding sides
in proportion,

BP / DP = AP / CP,

and the result follows.

### Related pages in this website:

Summary of geometrical theorems

The other Intersecting Chords
Theorem is a generalization of the central angle theorem.

### Internet references

Cut-the-knot:
Intersecting Chords Theorem

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Graeme McRae.