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Ptolemy's theorem
For a cyclic quadrilateral, the sum of the products of the two pairs of opposite sides equals the product of the diagonals.
A
B
×
C
D
+
B
C
×
D
A
=
A
C
×
B
D
AB \times CD + BC \times DA = AC \times BD
A
B
×
C
D
+
B
C
×
D
A
=
A
C
×
B
D
.
If
A
B
C
D
ABCD
A
B
C
D
is a rectangle, this reduces to Pythagoras's theorem.