Circles - Revision Notes

 CBSE Class 09 Mathematics

Revison Notes
CHAPTER 10
CIRCLES

  • Circles and its Related Terms : A Review
  • Angle Subtended by the chord at a Point
  • Perpendicular from the centre to a Chord
  • Circle through three given points.
  • Equal Chords and their distances from the Centre
  • Angle Subtended by an Arc of a Circle
  • Cyclic Quadrilaterals
     
  • Circle - Circle is a locus of such points which are at equidistant from a fixed point in a plane. Also, a circle is the colleciton of those points in a plane that are at a given constant distance from a given fixed-point in the plane. The fixed point is called the centre and the given distance is called the radius of the circle.
  • Concentric circles - Circles having same centre and different radii area called concentric circles.
  • Arc - A continuous piece of a circle is called an arc of the circle.
  • Chord - A line segment joining any two points on a circle is called the chord of the circle.
  • A chord passing through the centre of a circle is called the diameter of the circle.
  • A diameter of a circle divides it into two equal parts which are arcs. Each of these two arcs is called a semi-circle.
  • Two arcs of a circle  are called congruent if they have the same degree of  measure.
  • If two arcs are equal,then their corresponding chords are also equal.
  • The perpendicular drawn from centre to  the chord of circle bisects the chord and vice-versa.
  • There is one and only one circle passing through three non-collinear points.
  • Equal chords of circle are equidistant from centre.
  • If two circles intersect in two points, then the line through the centres is perpendicular to the common chord.
  • The angle subtended by an arc at the centre of circle is twice the angle  subtended at remaining part of circumference.
  • Any two angles in the same segment of the circle are equal.
  • Equal chords of a circle subtend equal angle at the centre.
  • Out of two chords of a circle, the larger chord is nearer to the centre.
  • Angle of semicircle is right angle.
  • Equal chords of circle subtend equal angle at the centre of circle.
  • If  all the vertices of a quadrilateral lies on the circumference of circle, then quadrilateral  is called cyclic.
  • In a cyclic quadrilateral the sum of opposite angles is 180o and vice-versa.
  • The exterior angle of a cyclic quadrilateral is equal to the  interior opposite angle.