Linked from

The 21 pages that link to Cyclic quadrilateral, each with the reason it gives.

• CircumcircleRelated: A triangle’s circumcircle can contain a fourth point, forming a cyclic quadrilateral.

• Inscribed angle theoremBroader topic: Its opposite angles subtend complementary arcs and therefore sum to 180 degrees.

• Ptolemy's theoremNarrower topic: The theorem applies precisely when all four vertices lie on a common circle.

• QuadrilateralBroader topic: Opposite angles in this special case are supplementary.

• ParallelogramCompared with: A cyclic parallelogram must be a rectangle, showing how an added condition narrows the class.

• Brahmagupta's formulaBroader topic: Checking this condition prevents misuse on a general quadrilateral.

• Miquel's theoremRelated: Circle membership can be proved through equal directed angles in the constituent triangles.

• Miquel pointRelated: Angle relations in cyclic quadrilaterals establish the circles' shared point.

• Ptolemy's inequalityBroader topic: These quadrilaterals are precisely the standard equality cases.

• Bretschneider's formulaBroader topic: For this special case, the angle correction vanishes and the formula reduces to Brahmagupta's.

• Euler's quadrilateral theoremBroader topic: Its equal diagonal-midpoint distances offer a useful special case of the general formula.

• Butterfly theoremRelated: Many proofs organize the chord endpoints into cyclic quadrilaterals.

• Six circles theoremBroader topic: The proof reduces successive circle incidences to cyclic quadrilaterals.

• Casey's theoremRelated: Its opposite-side products give the classical setting that Casey's theorem extends.

• Constant chord theoremRelated: Its equal angles can imply equal opposite-side chords through the theorem.

• Conway circle theoremBroader topic: The theorem’s concyclicity can be checked through equal-angle or opposite-angle conditions.

• Five circles theoremRelated: Cyclic quadrilaterals frequently appear as intermediate figures in the theorem’s proofs.

• Haruki's theoremRelated: Such quadrilaterals commonly arise when two circles provide shared intersection points and auxiliary vertices.

• Japanese theoremBroader topic: Its opposite angles are supplementary, supplying the angle relations used in the proof.

• Japanese theorem for cyclic polygonsBroader topic: The theorem’s first nontrivial polygon case is a cyclic quadrilateral.

• Seven circles theoremRelated: Several local four-point circle relations can appear inside the seven-circle arrangement.