Class 9 Maths - BIHAR
Circles
The chapter 'Circles' in Class 9 Bihar Board Mathematics introduces students to the geometric properties of a circle and its related terms like chords, arcs, sectors, and segments. You will learn important theorems regarding the perpendicular from the centre to a chord, equal chords and their distances from the centre, and angles subtended by arcs at the centre and circumference. Mastering these concepts is crucial for solving both theoretical proofs and numerical problems. This chapter carries significant weightage in the BSEB Class 9 annual examinations, often featuring in both short-answer and long-answer proof-based questions.
Start Learning FreeKey Concepts
Perpendicular from Centre to Chord
The 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 Distances
Equal chords of a circle are equidistant from the centre, and conversely, 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 always equal to one another.
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 Bihar (BSEB) Class 9 mathematics examinations, the chapter 'Circles' typically carries around 6 to 10 marks. Questions usually include 1-mark objective questions, 2-mark short answer questions based on angle properties, and 4-mark or 5-mark long answer questions requiring formal geometric proofs of major theorems like the cyclic quadrilateral property or the angle at the centre theorem.
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.
Why is the sum of opposite angles in a cyclic quadrilateral 180 degrees?
This can be proven by using the theorem that the angle subtended by an arc at the centre is twice the angle subtended at the circumference, linking the opposite angles to the total angle of 360 degrees around the centre.
How do I approach geometry proof questions in the BSEB exam?
Always start by clearly writing 'Given', 'To Prove', and any necessary 'Construction'. Use standard geometric theorems as reasons for each step in your proof to ensure full marks.
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