Class 9 Maths - TAMILNADU
Circles
The Circles chapter in Class 9 Mathematics under the Tamil Nadu Samacheer Kalvi syllabus introduces students to the fundamental geometric properties of circles. You will explore terms like chords, arcs, sectors, and segments, along with important theorems regarding perpendiculars from the centre to a chord, equal chords and their distances, and angles subtended by arcs at the centre and circumference. Mastering this chapter is essential for board exams as it builds strong foundational logic for coordinate geometry and circle theorems in Class 10. It frequently features in both short-answer and geometric proof-based questions.
Start Learning FreeKey Concepts
Perpendicular from Centre to Chord
A perpendicular drawn from the centre of a circle to a chord always bisects the chord, and conversely, the line joining the centre to the midpoint of a chord is perpendicular to the chord.
Equal Chords and Their Distance from Centre
Equal chords of a circle (or of congruent circles) are equidistant from the corresponding 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 called cyclic if all four of its vertices lie on a single circle, and the sum of either pair of opposite angles of a cyclic quadrilateral is 180 degrees.
Important Formulas
Board Exam Info
In the Tamil Nadu Samacheer Kalvi Class 9 Mathematics examinations, the Circles chapter typically carries around 8 to 12 marks. Questions usually include 1-mark objective questions, 2-mark or 5-mark short answers involving numerical calculations based on circle properties, and geometric reasoning or proof questions based on theorems.
Frequently Asked Questions
What is the difference between a chord and a secant?
A chord is a line segment whose endpoints both lie on the circle, whereas a secant is a line that intersects the circle at two distinct points and extends indefinitely beyond them.
Are all circles similar?
Yes, all circles are similar because they have the same shape, differing only in size depending on the length of their radii.
How do I prove a quadrilateral is cyclic?
You can prove a quadrilateral is cyclic by showing that the sum of any pair of its opposite angles equals 180 degrees, or by showing that an exterior angle is equal to the interior opposite angle.
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