NCERT Notes for Class 9 Maths Chapter 11 Circles
![NCERT Notes for Class 9 Maths Chapter 11 Circles NCERT Notes for Class 9 Maths Chapter 11 Circles](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj0XHxTPFSRtYiBWyYPJBQah1EcjJZJSoecBCUUnJ7DFRcv3V1iLKK27WqN83WWp8Q5UWXqwY-BDQr3uqTlasc6OB7vUF_NogF_E48faeY4hLUszeW2eNOhkFfCE5mfwPW3l3h2FuMnyhZCJeSYYZFjuQjlqHjgNs7Quh60cJuzKU_RHU6XzW9ErQTyZew1/s16000/circles-revision-notes-class9-maths.jpg)
Class 9 Maths Chapter 11 Circles Notes
Chapter Name | Circles Notes |
Class | CBSE Class 9 |
Textbook Name | Mathematics Class 9 |
Related Readings |
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Circle
Circle is the collection of all points in a plane, which are equidistant from a fixed point in the plane. The fixed point is called the centre O and the given distance is called the radius r of the circle.
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Concentric circles
Circles having same centre and different radii are called concentric circles.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjCPfoDw6F3ir1_PHjVCQNTH3Etrm29FFF1pGnoSewzgbo0TbvEolrrhEk13UM3EsgbdEvLkrseTYP6_iw3tJdANJnjgqLdAPyYsSNCt8o4dXNCOjw4ZXqx9y9dobVkcjz_KpmbiofIdsihBtm9z7TjoCFRQg83t6Nz0iJwSZlB3NGiN4ws92j1QZdenBQ/w187-h187/Ncert%20notes%20class%209%20math%20chapter%2011%20Circles%20img%202.jpg)
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.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-Q1BpNTP7omg9QHZizyD5AtdFSau7rGA141J_CMeb-uk48Lowb13lNnlxUr4z40qEc8AMasM4tAPCo-XPNPqFVYRT665FdffvIufEMMPneAdOtA12psn-ozAC-8EvkD0fNYx7FVraIG854_JJ8ezZK0SUz6ItiXd9zty0hAmxX5HShMJ3XAYeZPlR9xQ/w177-h172/Ncert%20notes%20class%209%20math%20chapter%2011%20Circles%20img%203.jpg)
Diameter: A chord passing through the centre of a circle is called the diameter of the circle.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgHuem-w8Y3bNEwd4wuAqG2lkmEuIsxFcMZ2YObpu17hhICiZ2SMwzTC1z2Ypd59PDa5goaXxfOckKBFhcHFMG55cCkRWbcbOl-ON1AyUtAQ-g7p80tAwuxISAWYdOkRhpXZp9umG6NkjjfnduORSrDUMqmZE7QDWAiPndRp1hL21Hqfkaqhoc1QacGPns/w193-h167/Ncert%20notes%20class%209%20math%20chapter%2011%20Circles%20img%204.jpg)
Semicircle
- Angle of semicircle is right angle.
- If two arcs are equal, then their corresponding, chords are also equal.
Theorem 10.1: Equal chords of a circle subtend equal angle at the centre of the circle.
Theorem 10.2: If the angles subtended by the chords of a circle at the centre are equal, then the chords are equal.
Theorem 10.3: The perpendicular drawn from centre to the chord of circle bisects the chord.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhKW1YVJQfWXHHIUTDR0z-laVJCqnliU6Y_vzR9ykr1qwAUo3QLvMGaC_LAHERDFL2wOP0kUv5nGYydntZL7cD_LeY9cy4DcLT8QnFXNMkjX7QJIwssQBNtBDMXWZpa099t1QH9v0Hn_lC57-68-35mhTUsoxCW_eu_ej4nizQWqqCvwsaL6-o2r1xpiUo/w201-h196/Ncert%20notes%20class%209%20math%20chapter%2011%20Circles%20img%205.jpg)
Theorem 10.4: The line drawn through the centre of a circle to bisect a chord is perpendicular to the chord.
Theorem 10.5: There is one and only one circle passing through three non-collinear points.
Theorem 10.6: Equal chords of circle are equidistant from centre.
Theorem 10.7: Chords equidistant from the centre of a circle are equal in length.
If two circles intersect in two points, then the line through the centres is perpendicular to the common chord.
Theorem 10.8: The angle subtended by an arc at the centre of circle is twice the angle subtended at remaining part of circumference.
Theorem 10.9: Any two angles in the same segment of the circle are equal.
Theorem 10.10: If a line segment joining two points subtends equal angles at two other points on the same side of the line containing the line segment, the four points lie on a circle (i.e., they are concyclic).
Cyclic Quadrilateral
If all the vertices of a quadrilateral lie on the circumference of circle, then quadrilateral is called cyclic.
Theorem 10.11: In a cyclic quadrilateral the sum of opposite angles is 180°.
Theorem 10.12: In a quadrilateral if the sum of opposite angles is 180°, then quadrilateral is cyclic.
- The exterior angle of a cyclic quadrilateral is equal to the interior opposite angle.