Class 9 Maths - CBSE
Circles
The Class 9 CBSE chapter on Circles explores the geometric properties of a round figure and its parts like chords, arcs, segments, and sectors. Students learn important theorems regarding perpendiculars from the centre to a chord, equal chords and their distances from the centre, and angles subtended by arcs at the centre versus the circumference. This chapter forms the foundation of advanced geometry in Class 10, particularly involving tangents and secants. It carries significant weight in board-pattern school exams, requiring students to apply logical reasoning, definitions, and theorems to solve both numerical and proof-based geometry questions accurately.
Start Learning FreeKey Concepts
Chord and Arc Properties
Equal chords of a circle subtend equal angles at the centre, and conversely, if their angles are equal, the chords are equal.
Perpendicular from Centre to Chord
A perpendicular drawn from the centre of a circle to a chord always bisects the chord, and the line joining the centre to the midpoint of a chord is perpendicular to it.
Equal Chords and Distance from Centre
Equal chords of a circle (or of congruent circles) are equidistant from the centre (or centres).
Angle Subtended by an Arc
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
Angles in the same segment of a circle are always equal to one another.
Cyclic Quadrilateral
A quadrilateral is cyclic if all its four vertices lie on a circle, and the sum of either pair of opposite angles of a cyclic quadrilateral is 180 degrees.
Important Formulas
Board Exam Info
In CBSE Class 9 mathematics examinations, the chapter on Circles typically carries around 6 to 8 marks. Questions frequently appear as short-answer proofs (2-3 marks) and long-answer multi-step problem-solving questions (4 marks), often combining cyclic quadrilaterals and angle sum properties.
Frequently Asked Questions
What is the difference between a segment and a sector?
A sector is the region enclosed by two radii and an arc, whereas a segment is the region enclosed by a chord and an arc.
How do I prove a quadrilateral is cyclic?
You can prove it by showing that the sum of either pair of opposite angles is 180 degrees, or by proving that an exterior angle equals the interior opposite angle.
Are all circles similar?
Yes, all circles are similar because they have the same shape, differing only in their radii or sizes.
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