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Chapter Summary

Angles In A Circle And Cyclic Quadrilateral — Chapter Summary

NIOS · Class 10 · Maths

Summary of Angles In A Circle And Cyclic Quadrilateral for NIOS Class 10 Maths. Part of the NIOS Class 10 Maths syllabus.

41 questions28 flashcards8 formulas & key relations5 concepts

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A diagram illustrating the definitions of central angle and inscribed angle, showing an arc, the center of the circle, and a point on the remaining part of the circle.
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Overview

Central angles and inscribed angles are the main ideas in circle geometry. A central angle is formed at the centre of a circle by radii joining the ends of an arc or chord. An inscribed angle is formed on the remaining part of the circle by the same arc or chord. The chapter also develops the idea o

Key Concepts

The angle made at the centre

The angle made at the centre of a circle by the radii at the end points of an arc or a chord is called the central angle. If an arc subtends a central

The angle subtended by an arc

The angle subtended by an arc or chord on any point on the remaining part of the circle is called an inscribed angle. It is formed on the circle, not

The angle subtended at the centre

The angle subtended at the centre of a circle by an arc is double the angle subtended by it on any point on the remaining part of the circle. In symbo

A semicircle has degree measure 180°

A semicircle has degree measure 180°, so the inscribed angle subtending a diameter is 90°. In symbols, 2∠PBQ = ∠POQ = 180° ⇒ ∠PBQ = 90°.

Angles subtended by the same chord

Angles subtended by the same chord or arc in the same segment of a circle are equal. If two angles stand on the same chord and lie on the same side of

Learning Objectives

  • Identify central angles and inscribed angles
  • Use the fact that the angle subtended at the centre is double the angle subtended at the circle
  • Find the degree measure of minor arcs, semicircles, and major arcs
  • Use the formula for the length of an arc
  • Apply the theorem that angles in the same segment are equal

Frequently Asked Questions

What are the important topics in Angles In A Circle And Cyclic Quadrilateral for NIOS Class 10 Maths?
Key topics in Angles In A Circle And Cyclic Quadrilateral include Angles in a Circle, Concyclic Points and Cyclic Quadrilateral. Study these first, then practise questions on each for the NIOS Class 10 board exam.
How should I revise Angles In A Circle And Cyclic Quadrilateral for the NIOS Class 10 board exam?
Learn the core ideas first, then work through the 41 practice questions on Angles In A Circle And Cyclic Quadrilateral. Revise definitions regularly and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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