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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.
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]
Euler's quadrilateral theorem or Euler's law on quadrilaterals, named after Leonhard Euler (1707–1783), describes a relation between the sides of a convex quadrilateral and its diagonals. It is a generalisation of the parallelogram law which in turn can be seen as generalisation of the Pythagorean theorem .
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.
Only 45 per cent knew pitting or thickening of the breast skin could also be a warning sign of breast cancer. ... In the US, the lifetime risk of having breast cancer for women is 13 per cent ...
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.
For the general quadrilateral (with four sides not necessarily equal) Euler's quadrilateral theorem states + + + = + +, where is the length of the line segment joining the midpoints of the diagonals. It can be seen from the diagram that x = 0 {\displaystyle x=0} for a parallelogram, and so the general formula simplifies to the parallelogram law.