NCERT Exemplar Solution for Class 9 Maths Chapter 10 – Circles
The tenth chapter of Class 9 Mathematics, Circles, is an essential part of geometry that introduces students to theorems and properties related to chords, tangents, and angles. This chapter develops logical reasoning and proof-based problem-solving skills. With the help of NCERT Exemplar Class 9 Maths Solutions, learners can practice advanced-level problems, while NCERT Solutions for Class 9 Maths ensure stepwise clarity for each theorem and exercise. The chapter begins with the basic definition of a circle and its components, such as radius, diameter, chord, arc, and sector. Students learn how these elements are interrelated and form the foundation of circle geometry.
A key subtopic is the theorems related to chords. Students study results such as:
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Equal chords of a circle subtend equal angles at the center.
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If two chords are equal, then they are equidistant from the center.
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The perpendicular drawn from the center of a circle to a chord bisects the chord.
Through NCERT Solutions for Class 9 Maths, each theorem is explained with diagrams and proofs, making them easy to understand and apply.
Another important section of this chapter deals with angles subtended by chords and arcs. Students learn theorems like “the angle subtended by an arc at the center is twice the angle subtended at the remaining part of the circle” and “angles subtended by a chord in the same segment are equal.” These theorems are widely used in solving higher-level problems. The chapter also includes the study of cyclic quadrilaterals, which are quadrilaterals whose vertices lie on a circle. The property that “the sum of opposite angles of a cyclic quadrilateral is 180°” is an important theorem frequently used in competitive exams. Exemplar questions provide higher-order applications of these theorems, enhancing analytical skills. Although the topic of tangents is introduced in higher classes, this chapter builds the groundwork by familiarizing students with related concepts. By solving NCERT Exemplar Class 9 Maths Solutions, learners gain practice with reasoning-based proofs, while textbook solutions provide accuracy and clarity. In conclusion, Chapter 10 develops strong logical thinking and problem-solving abilities. With consistent practice using NCERT Solutions for Class 9 Maths and exemplar problems, students can confidently master theorems of circles, ensuring excellent preparation for board and competitive exams.