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NCERT Solutions for Class 9 Maths Chapter 10

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NCERT Solutions for Class 9 Maths Chapter 10 Circles – वृत in PDF form to free download. NCERT Solutions of other subjects are also available free to use or download. Solutions are prepared for CBSE & UP Board students appearing in 2018-2019 CBSE Exams and following the updated NCERT Books.

NCERT Solutions for Class 9 Maths Chapter 10 Circles - वृत

NCERT Solutions for Class 9 Maths Chapter 10

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Class 9 Maths Chapter 10 Circles – वृत Solutions

Hindi Medium and English Medium Solutions

Important Terms and Theorems on Circles – वृत
  • Circle: A circle is the collection of all points in a plane, which are at a fixed distance from a fixed point in the plane.
    1. Diameter: It is the longest chord of the circle.
    2. Circumference: The length of complete circle is called its circumference.
    3. Arc: A piece of circle between two point is called arc.
    4. Segment: The region between a chord and either of its arcs is called a segment of circular region.
  • Properties related to CIRCLE
    • Equal chords of a circle subtend equal angles at the centre.
    • If the angles subtended by two chords of a circle at the centre are equal, the chords are also equal.
    • The perpendicular from the centre of a circle to a chord bisects the chord.
    • The line drawn 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 chords of a circle are equidistant from the centre and cords equidistant from the centre of a circle are equal.
  • 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 arcs are congruent.
  • Congruent arcs of a circle subtend equal angles at the centre.
  • 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.
  • Angle in a semi-circle is a right angle.
  • The sum of either pair of opposite angles of a cyclic quadrilateral is 180 and if the sum of a pair of opposite angles of a quadrilateral is 180, then the quadrilateral is cyclic.

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