If a quadrilateral is cyclic then the product of the lengths of its diagonals is equal to the sum of the products of the lengths of the pairs of opposite sides. Square · Proofs · Corollaries · Corollary 1. Pythagoras's...

Ptolemy's theorem states the relationship between the diagonals and the sides of a cyclic quadrilateral. It is a powerful tool to apply to problems about ...

Ptolemy's theorem gives a relationship between the side lengths and the diagonals of a cyclic quadrilateral; it is the equality case of Ptolemy's Inequality.

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Опубликовано: 23 апр. 2020 г.

Ptolemy's theorem: For a cyclic quadrilateral (that is, a quadrilateral inscribed in a circle), the product of the diagonals equals the sum of the products of ...

Ptolemy's Theorem states that in a cyclic quadrilateral, the sum of the products of opposite pairs of sides is equal to the product of the diagonals. In the ...

In a more gen- eral context, Ptolemy's Theorem is the inequality lABl x lCDl + lADl x I BCI >. lACl x I BDI, where equality occurs if and only if A, B, C, D lie ...

Let a convex quadrilateral ABCD be inscribed in a circle. Then the sum of the products of the two pairs of opposite sides equals the product of its two ...

In words: “The sum of the products of opposite pairs of sides of a cyclic quadrilateral is equal to the product of the diagonals” (see Figure 1). The crucial ...

Proposition. Let a cyclic quadrilateral ABCD. Then the sum of the products of the two pairs of opposite sides equals the product of its two diagonals.