Unit 12 Angle in a Segment of a Circle Master Solutions
Unit 12 Angle in a Segment of a Circle, is second last unit of Class 10 mathematics. In this unit students explore essential properties of angles and arcs within a circle. This unit covers key concepts, including the central angle and corresponding arcs, angles in the same segment, angles related to semi-circles, and the properties of inscribed quadrilaterals. These theorems are vital for understanding circle geometry and provide a foundation for solving complex problems. This post not only explains these principles but also includes complete solutions for the exercises, helping students build confidence and proficiency in these circle-related concepts.
Table of Contents
PDF Solutions
Multiple Choice Questions Test for Unit 12
To reinforce your understanding of Unit 12 Angle in a Segment of a Circle, we’ve included a Multiple Choice Questions (MCQ) test designed to cover the core concepts. This test includes questions on the relationship between central angles and arcs, equality of angles within the same segment, properties of angles in semi-circles, and the supplementary nature of opposite angles in inscribed quadrilaterals. Attempting these questions can solidify your grasp of each theorem, and reviewing the solutions will further clarify how to apply these ideas in various scenarios.
Key Concepts of Unit 12 Angle in a Segment of a Circle
Central Angle and Corresponding Arc:
- Statement: The measure of the central angle of a minor arc of a circle is double that of the angle subtended by the corresponding major arc.
- Explanation: The angle at the center of the circle (central angle) that looks at a small part of the circle (minor arc) is twice as big as the angle that looks at the bigger part of the circle (major arc).
Angles in the Same Segment:
- Statement: Any two angles in the same segment of a circle are equal.
- Explanation: If two angles are formed by drawing lines from the ends of a chord (a line inside the circle), and those angles are on the same side of the chord, they are equal.
Angles Related to Semi-Circles:
- Statement: The angle in a semi-circle is a right angle; in a segment greater than a semi-circle, it is less than a right angle; and in a segment less than a semi-circle, it is greater than a right angle.
- Explanation: If an angle is formed by drawing a line to the edge of a semi-circle, it’s always a right angle. If it’s in a bigger segment, it’s smaller than a right angle, and in a smaller segment, it’s bigger than a right angle.
Opposite Angles in an Inscribed Quadrilateral:
- Statement: The opposite angles of any quadrilateral inscribed in a circle are supplementary.
- Explanation: If you draw a four-sided shape inside a circle, the opposite angles add up to 180 degrees.
List of formulas used in this chapter is here
Unit 13 solutions are here
Mastering Unit 12 Angle in a Segment of a Circle equips students with valuable skills for solving problems involving circles in geometry. The solutions provided in this post help reinforce your understanding, allowing you to approach related questions with confidence. With regular practice, these concepts will become second nature, making it easier to handle both classroom exercises and exam questions. Don’t forget to revisit these key points regularly and refer to additional resources, like Math is Fun’s circle theorems guide, for extra examples and explanations. By strengthening your knowledge of these theorems, you’ll be well-prepared for any challenge involving circle geometry. Now lets move on the the final unit of the textbook of class 10 mathematics.