Class 9 Maths - HARYANA
Circles
The chapter 'Circles' in Class 9 Mathematics under the Haryana Board (BSEH) builds a strong geometric foundation by exploring the properties of circles, chords, arcs, and angles subtended by them. Students learn essential theorems regarding perpendiculars from the centre to a chord, equal chords and their distances, angles subtended by an arc at the centre and circumference, cyclic quadrilaterals, and angle properties in semi-circles. This chapter is vital for board exams as it tests logical deduction and theorem-based proof writing. Scoring well in this chapter requires a clear understanding of geometric reasoning and step-by-step problem-solving skills.
Start Learning FreeKey Concepts
Chord Properties
The perpendicular drawn from the centre of a circle to a chord bisects the chord, and conversely, the line drawn through the centre to bisect a chord is perpendicular to the chord.
Equal Chords and Distance
Equal chords of a circle (or of congruent circles) are equidistant from the centre and vice versa.
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 a right angle (90 degrees).
Cyclic Quadrilaterals
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 the Haryana Board (BSEH) Class 9 Mathematics examination, the 'Circles' chapter typically carries around 6 to 8 marks. Common question types include 1-mark multiple-choice questions, 2-mark short answer questions based on finding unknown angles, and 4-mark long answer questions requiring formal proofs of important theorems or riders.
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 a circle at two distinct points and extends indefinitely.
Are theorem proofs asked in the BSEH Class 9 exam?
Yes, direct proofs of important theorems, such as the angle subtended by an arc at the centre property or properties of cyclic quadrilaterals, are frequently asked in the 4-mark section.
How do I prove a quadrilateral is cyclic?
You can prove a quadrilateral is cyclic by showing that the sum of any pair of opposite angles is 180 degrees, or by proving that an exterior angle is equal to the interior opposite angle.
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