Class 9 Maths - ANDHRA-PRADESH
Circles
The Class 9 Mathematics chapter on 'Circles' for Andhra Pradesh (BSEAP) students explores the fundamental geometric properties of a circle and its parts. You will learn about chords, arcs, sectors, cyclic quadrilaterals, and the relationships between angles subtended by arcs at the center and circumference. This chapter is vital for your board exams as it tests both your conceptual understanding and geometric reasoning through theorem-based proofs and riders. Mastering these properties builds a strong foundation for advanced geometry in Class 10 and frequently appears in both short-answer and essay questions.
Start Learning FreeKey Concepts
Perpendicular from Centre to Chord
The perpendicular drawn from the centre of a circle to a chord 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 Distances
Equal chords of a circle (or of congruent circles) are equidistant from the centre, and chords that are equidistant from the centre are equal in length.
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 equal, and the angle in a semicircle is always a right angle (90 degrees).
Cyclic Quadrilateral
A quadrilateral is called cyclic if all four of its 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 the Andhra Pradesh (BSEAP) Class 9 mathematics examinations, the chapter on 'Circles' usually carries around 8 to 12 marks. Questions commonly appear as direct theorem proofs, 2-mark or 4-mark numerical problems based on finding unknown angles, and construction or reasoning questions involving cyclic quadrilaterals.
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 straight line that intersects the circle at two distinct points and extends indefinitely outside it.
Are all angles in the same segment always equal?
Yes, any two angles subtended by the same arc at different points on the circumference in the same segment are always equal to each other.
How do I prove that a quadrilateral is cyclic?
You can prove a quadrilateral is cyclic by showing that the sum of either pair of its opposite angles is 180 degrees, or by demonstrating that an exterior angle is equal to the interior opposite angle.
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