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It states that in a cyclic quadrilateral , as shown in the accompanying figure, the sum of the products of the lengths of opposite sides is equal to the product of the lengths of the diagonals. In the special cases of one of the diagonals or sides being a diameter of the circle, this theorem gives rise directly to the angle sum and difference ...
More generally, if the quadrilateral is a rectangle with sides a and b and diagonal d then Ptolemy's theorem reduces to the Pythagorean theorem. In this case the center of the circle coincides with the point of intersection of the diagonals. The product of the diagonals is then d 2, the right hand side of Ptolemy's relation is the sum a 2 + b 2.
Equidiagonal quadrilateral: the diagonals are of equal length. Bisect-diagonal quadrilateral: one diagonal bisects the other into equal lengths. Every dart and kite is bisect-diagonal. When both diagonals bisect another, it's a parallelogram. Ex-tangential quadrilateral: the four extensions of the sides are tangent to an excircle.
It may also be caused by therapies such as radiation or chemotherapy. With competent management, cancer pain can be eliminated or well controlled in 80% to 90% of cases, but nearly 50% of cancer patients in the developed world receive less than optimal care. Worldwide, nearly 80% of people with cancer receive little or no pain medication. [15]
Equivalently, a quadrilateral has equal diagonals if and only if it has perpendicular bimedians, and it has perpendicular diagonals if and only if it has equal bimedians. [7] Silvester (2006) gives further connections between equidiagonal and orthodiagonal quadrilaterals, via a generalization of van Aubel's theorem. [8]
Cancer is a northern sign, and its opposite sign is Capricorn. [5] [6] [7] Cancer is a cardinal sign. Water is the element associated with Cancer, [8] and, alongside Scorpio and Pisces, it forms the water trigon. [9] The water trigon is one of four elemental trigons in the zodiac, with the other three being fire, earth, and air. [10]
3 Zodiac Signs Setting Boundaries or Most Impacted by Mars Entering Cancer (9/4) Read for your zodiac sign. Consider your Sun, Moon, and Rising signs if you know them.
A rhombus has an inscribed circle, while a rectangle has a circumcircle. A rhombus has an axis of symmetry through each pair of opposite vertex angles, while a rectangle has an axis of symmetry through each pair of opposite sides. The diagonals of a rhombus intersect at equal angles, while the diagonals of a rectangle are equal in length.