If the intersection of any two perpendicular chords divides one chord into lengths a and b and divides the other chord into lengths c and d, then a 2 + b 2 + c 2 + d 2 equals the square of the diameter.If the intersection of any two chords divides one chord into lengths a and b and divides the other chord into lengths c and d, then ab = cd.Among all the circles with a chord AB in common, the circle with minimal radius is the one with diameter AB.The diameter is the longest chord of the circle.An inscribed angle subtended by a diameter is a right angle (see Thales' theorem).For a cyclic quadrilateral, the exterior angle is equal to the interior opposite angle.If two angles are inscribed on the same chord and on opposite sides of the chord, then they are supplementary.If two angles are inscribed on the same chord and on the same side of the chord, then they are equal.If a central angle and an inscribed angle of a circle are subtended by the same chord and on the same side of the chord, then the central angle is twice the inscribed angle.The line segment through the centre bisecting a chord is perpendicular to the chord.A perpendicular line from the centre of a circle bisects the chord.The perpendicular bisector of a chord passes through the centre of a circle equivalent statements stemming from the uniqueness of the perpendicular bisector are:.Chords are equidistant from the centre of a circle if and only if they are equal in length.In Cartesian coordinates, it is possible to give explicit formulae for the coordinates of the centre of the circle and the radius in terms of the coordinates of the three given points. Through any three points, not all on the same line, there lies a unique circle. Download 470,072 Circle Outline Stock Illustrations, Vectors & Clipart for FREE or amazingly low rates New users enjoy 60 OFF.Thought of as a great circle of the unit sphere, it becomes the Riemannian circle.The circle that is centred at the origin with radius 1 is called the unit circle.The constants of proportionality are 2 π and π respectively.The area enclosed and the square of its radius are proportional.A circle circumference and radius are proportional.The group of rotations alone is the circle group T. Its symmetry group is the orthogonal group O(2, R). The circle is a highly symmetric shape: every line through the centre forms a line of reflection symmetry, and it has rotational symmetry around the centre for every angle. The circle is the shape with the largest area for a given length of perimeter (see Isoperimetric inequality).Usually, the radius is required to be a positive number. The distance between any point of the circle and the centre is called the radius. A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
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