Cyclic polygon: Difference between revisions
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In [[plane geometry]], a '''cyclic polygon''' is a [[polygon]] whose vertices all lie on one [[circle]]. The centre of the circle is the [[circumcentre]] of the polygon. | In [[plane geometry]], a '''cyclic polygon''' is a [[polygon]] whose vertices all lie on one [[circle]]. The centre of the circle is the [[circumcentre]] of the polygon. | ||
Revision as of 20:27, 31 January 2009
In plane geometry, a cyclic polygon is a polygon whose vertices all lie on one circle. The centre of the circle is the circumcentre of the polygon.
Every triangle is cyclic, since any three (non-collinear) points lie on a unique circle.
Cyclic qusdrilateral
A cyclic quadrilateral is a quadrilateral whose four vertices are concyclic. A quadrilateral is cyclic if and only if pairs of opposite angles are supplementary (add up to 180°, π radians). Ptolemy's theorem states that in a cyclic quadrilateral ABCD, the product of the diagonals is equal to the sum of the two products of the opposite sides:
