circles

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A circle is a simple shape of Euclidean geometry consisting of those points in a plane which are equidistant from a given point called the center. Circles

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History The circle has been known since before the beginning of recorded history. It is the basis for the wheel, which, with related inventions such as gears, makes much of modern civilization possible. In mathematics, the study of the circle has helped inspire the development of geometry and calculus. Early science, particularly geometry and Astrology and astronomy, was connected to the divine for most medieval scholars, and many believed that there was something intrinsically "divine" or "perfect" that could be found in circles. Some highlights in the history of the circle are: 1700 BC – The Rhind papyrus gives a method to find the area of a circular field. The result corresponds to 256/81as an approximate value of π. 300 BC – Book 3 of Euclid's Elements deals with the properties of circles. 1880 – Lindemann proves that π is transcendental, effectively settling the millennia-old problem of squaring the circle.

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The common distance of the points of a circle from its center is called its radius. A chord of a circle is a line segment whose two endpoints lie on the circle. The largest chord in a circle passing through the circle's centre is the diameter. A tangent to a circle is a straight line that touches the circle at a single point. A secant is an extended chord: a straight line cutting the circle at two points. Terminology

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An arc of a circle is any connected part of the circle's circumference. A sector is a region bounded by two radii and an arc lying between the radii. a segment is a region bounded by a chord and an arc lying between the chord's endpoints.

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Properties of circle

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· Equal chords subtend equal angles at the centre of the circle. ·If angles subtended by the chords of a circle at the centre are equal, then the chords are equal. 1) Angles subtended by a chord at a point

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The perpendicular from the centre of a circle to a chord bisects the chord or The line drawn through the centre of a circle to bisect a chord is perpendicular to a chord 2) Perpendicular from the centre to a chord

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Equal chords of a circle are equidistant from the centre or Chords equidistant from the centre are equal in length 3) Equal chords and their distances from the centre

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The angle formed at the centre of the circle by lines originating from two points on the circle's circumference is double the angle formed on the circumference of the circle by lines originating from the same points. i.e. a = 2b. Angle at the Centre = 2*angle at the circumference 4) Angles subtended by an arc of a circle

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Angle formed from two points on the circumference is equal to other angle, in the same segment, formed from those two points. angles subtended by a line segment in the same segment are equal Angles in the same segment of a circle are equal or

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Angles formed by drawing lines from the ends of the diameter of a circle to its circumference form a right angle. So c is a right angle. Angle in a Semi-Circle is right angle

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5) Cyclic quadrilaterals A cyclic quadrilateral is a quadrilateral whose all vertices lie on a single circle and whose pair of opposite angles is supplementary. So here, ∟A + ∟C = 180˚ ∟B + ∟D = 180˚

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Thank you