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Ptolemy's Theorem
Toolkit 59
Ptolemy's Theorem
A quadrilateral
A
B
C
D
ABCD
A
B
C
D
is cyclic if and only if:
A
B
⋅
C
D
+
A
D
⋅
B
C
=
A
C
⋅
B
D
AB\cdot CD+AD\cdot BC=AC\cdot BD
A
B
⋅
C
D
+
A
D
⋅
B
C
=
A
C
⋅
B
D
Related Problems
Core
AMC 12A 2024 (Problem 19)
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