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Each pair of conjugate diameters of an ellipse has a corresponding tangent parallelogram, sometimes called a bounding parallelogram, formed by the tangent lines to the ellipse at the four endpoints of the conjugate diameters. All tangent parallelograms for a given ellipse have the same area.
Every line in projective geometry contains a point at infinity, also called a figurative point. The ellipse, parabola, and hyperbola are viewed as conics in projective geometry, and each conic determines a relation of pole and polar between points and lines. Using these concepts, "two diameters are conjugate when each is the polar of the ...
Since lines AC and BD are parallel, likewise for AD and CB, the quadrilateral ACBD is a parallelogram. Since lines AB and CD, the diagonals of the parallelogram, are both diameters of the circle and therefore have equal length, the parallelogram must be a rectangle. All angles in a rectangle are right angles.
No tangent line can be drawn through a point within a circle, since any such line must be a secant line. However, two tangent lines can be drawn to a circle from a point P outside of the circle. The geometrical figure of a circle and both tangent lines likewise has a reflection symmetry about the radial axis joining P to the center point O of ...
A polygon whose vertices are concyclic is called a cyclic polygon, and the circle is called its circumscribing circle or circumcircle. All concyclic points are equidistant from the center of the circle. Three points in the plane that do not all fall on a straight line are concyclic, so every triangle is a cyclic polygon, with a well-defined ...
For any isosceles trapezoid, tangent lines to the circumscribing circle at its four vertices form the four sides of a kite. This correspondence can also be seen as an example of polar reciprocation , a general method for corresponding points with lines and vice versa given a fixed circle.
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In general, any quadrilateral with perpendicular diagonals, one of which is a line of symmetry, is a kite. Every rhombus is a kite, and any quadrilateral that is both a kite and parallelogram is a rhombus. A rhombus is a tangential quadrilateral. [10] That is, it has an inscribed circle that is tangent to all four sides. A rhombus.