Class 9 Maths - MP
Circles
In the Class 9 Mathematics chapter on Circles for the Madhya Pradesh Board (MPBSE), students explore the geometric properties of circles. A circle is the collection of all points in a plane at a fixed distance from a fixed point. This chapter covers essential definitions like chords, segments, sectors, and arcs. Key theorems prove that equal chords subtend equal angles at the centre, perpendiculars from the centre bisect chords, and angles subtended by an arc at the centre are double the angles subtended at any point on the remaining part of the circle. Mastery of these concepts is crucial for scoring high in geometry.
Start Learning FreeKey Concepts
Chord and Arc Properties
Equal chords of a circle subtend equal angles at the centre, and conversely, if the angles subtended by chords at the centre are equal, the chords are equal.
Perpendicular from Centre to Chord
The perpendicular drawn from the centre of a circle to a chord always bisects the chord, and the line drawn through the centre to bisect a chord is perpendicular to the chord.
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 MPBSE Class 9 Mathematics board-aligned exams, the chapter on Circles typically carries around 6 to 8 marks. Questions generally include objective type questions, fill-in-the-blanks, short-answer questions based on applying circle theorems, and long-answer proof-based questions involving cyclic quadrilaterals or angle properties.
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 infinitely in both directions.
Are angles in the same segment always supplementary?
No, angles in the same segment are always equal, not supplementary. Opposite angles of a cyclic quadrilateral are supplementary.
How do I prove a quadrilateral is cyclic?
You can prove a quadrilateral is cyclic by showing that the sum of either pair of opposite angles is 180 degrees, or by showing that an exterior angle is equal to the interior opposite angle.
Learn Circles with Your AI Tutor
10 different ways to study this chapter. Free for 3 chapters per day.
Lecture
Key Points
Interactive
Quiz
Flashcards