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10. CIRCLES, ➢, , Circle: It is a collection of all points in a plane which are at a constant, distance from a fixed point., , ➢, , Centre: The fixed point is called the centre., , ➢, , Radius: The constant distance from the centre is called the radius., , ➢, , Chord: A line segment joining any two points on a circle is called chord of a, circle., The maximum length of a chord is equal to the length of the diameter., If a circle and a line have no common point, then the line is called a Nonintersecting line w.r.t the circle., , ➢, , Secant: A line intersect the circle in two points is called secant of the, circle., , ➢, , Tangent: A line touches the circle at only one point is called tangent to the, circle., There is only one tangent at a point on the circumference of the circle., The common point of the tangent and the circle is called the point of, contact., The line containing the radius through the point of contact of tangent is, called the normal to the circle at the point., There is no tangent to the circle passing through a point lying inside the, circle., There are exactly two tangents to a circle through a point lying outside the, circle., The length of the segment of the tangent from an external point and the, point of contact with the circle is called the length of the tangent., The lengths of tangents drawn from an external point to circle are equal., , ➢, , Cyclic quadrilateral: If all the vertices of a quadrilateral lie on a circle is, called cyclic quadrilateral., 1

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➢, , Alternate segment: The segment opposite to the angle formed by the, chord of a circle with the tangent at a point is called alternate segment for, that angle., , ➢, , Concentric circles: Circles having same centre., , ➢, , Important theorems:, i., , The tangent at any point of a circle is perpendicular to the radius through, the point of contact., , ii. A line drawn through the end point of a radius and perpendicular to it, is the, tangent to the circle., , iii., , The lengths of tangents drawn from an external point to a circle are equal., , iv., , The perpendicular from the centre of a circle to chord bisects the chord and it is, vice versa., , v., vi., , Equal chords of a circle are equidistant from the centre and it is vice versa., The angle subtended by an arc of a circle to the centre is twice the angle, subtended by the circumference of a circle., , vii., viii., , The angle in a semi-circle is a right angle., The angle subtended by an arc of a circle to the centre is twice the angle, subtended by the circumference of the circle, , ix., , Angles in the same segment of a circle are equal., , x., , The sum of any pair of opposite angles of a quadrilateral is 180 degrees., , 2