### 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

• 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 ${180}^{o}$ and vice-versa.
• The exterior angle of a cyclic quadrilateral is equal to the  interior opposite angle.