States that, for any two chords in a circle (AB and CD) that intersect at point X, AX×BX = CX×DX.

Proof:

- Angles AXC and DXB are congruent (by vertical angle theorem)
- Construct line segments AC and DB (by line postulate)
- Angles BAC and CDB are congruent (because they both intercept arc DB)
- Triangles AXC and DXB are similar (by AA postulate)
- AX/DX = CX/BX (by CLSFP postulate)
- AX×BX = CX×DX (by multiplication).

Q.E.D.