CIRCLES

CIRCLES

1. DEFINITION

   • circle is a plane figure bounded by one curved line ,and such that all straight lines drawn from a certain point within it to the bounding line are equal.The bounding line is called its circumference and the point,is it centre.

2. PARTS OF CIRCLE

   • DIAMETER: it is any line segment thatpasses through the centre of the circle and its end points line on the circle
   • RADIUS: It is any line segment from the circle's centre to the perimeter of the circle.
   • CHORD: A chord is a straight line segment whose both endpoints line on the perimeter of the circle.
   • SECTOR: A sector is the portion of the circle enclosed by two radii and an arc , where the smaller area is know as minor sector and larger area is known as major sector
   • SEGMENT: A segment is a region bounded by a chord of a circle and the intercepted arc of the circle.the smaller area is known as minor segment and the larger area is known as the major segment.

3. THEOREMS

   • Equal chords of a circle subtend equal angles at the centre.
   • The perpendicular from the centre of a circle to a chord bisects a chord.
   • If the angles subtended by the chords of a circle at the centre are equal , then the chords are equal.
   • The line draw through the centre of a circle to bisect a chord is perpendicular to the chord.
   • There is one and only one circle passing through three non-collinear points.
   • Equal of a circle are equidistant from the centre.

4. THEOREMS

   • Chords equidistant from the centre of a circle are equal in length.
   • The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.
   • Angles in the same segment of a circle are equal.
   • If a line segment joining two points subtends equal angles at two other points lying on the same side of the line containing the line segment ,the four points lie on a circle.
   • The sum of either pair of opposite angles of a cyclic quadrilateral is 180 degrees
   • If the sum of a pair of opposite of a quadrilateral is 180 degrees,the quadrilateral is cyclic.