If two chords intersect forming segments of length A and B for the first and C and D for the second, then A times B = C times D.
https://en.wikipedia.org/wiki/Intersecting_chords_theorem
This theorem also implies an essential property of cyclic quadrilaterals. The proof of the theorem furthermore implies that all cyclic quadrilaterals are formed by 2 pairs of similar triangles.
For further reference, see:
https://en.wikipedia.org/wiki/Brahmagupta%27s_formula
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