Circles Class 9 Notes Maths - Chapter 10
What Are Circles ?
The collection of all those points in a plane, which are equidistant from a fixed part in the same plane.
Circles having same centre and different radii.
Terms Related To Circle
- CHORD — PQ
- MINOR ARC – PQ
- MAJOR ARC – PRO
- Area between PQ (Chord & Arc) = MINOR Segment
- Area between PQ Chord & Arc PRQ = MAJOR Segment
- Figure 2, Area between OA, OB & Arc AB = MINOR Sector
- AREA between OA, Arc ACB & OB = MAJOR Sector
- Equal Chords of a circle subtends equal angles at the centre and vice versa.
- Equal Chords of a circle are equidistant from the centre and vice versa.
- The perpendicular drawn from the centre of the circle to a chord bisects the chord and vice versa.
- The angle subtended by an arc at the centre is double the angle subtended by it at any other point on the circumference of the circle.
- In a circle, angles in the same segment made by a chord are equal.
- The angle in a semi-circle made by diameter (or largest chord) is right angle.
- If two arcs of a circle are congruent, then their corresponding chords are equal and conversely if two chords of a circle are equal, then their corresponding areas are congruent.
- It two circles intersect in two points, then the line through the centres is perpendicular to the common chord.
- Congruent arcs of a circle subtend equal angles at the centre.