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NCERT Solutions for Class 10 Maths Chapter 12 – Areas Related to Circles, is an important chapter that covers a range of topics related to circles and their areas. By studying this chapter, students will learn about the different concepts related to the circumference and area of circles, as well as the relationship between the two. The solutions provided are designed to help students prepare effectively for CBSE exams and build a strong foundation for advanced study in Geometry. With step-by-step solutions and a variety of practice questions, students can improve their problem-solving skills and develop a deeper understanding of the subject.
In NCERT Solution For Class 10, Maths, Chapter 12 Areas Related To Circles, we shall solve and discuss questions related to the concepts of perimeter (circumference) and area of a circle and apply this knowledge in finding the areas of two special ‘parts’ of a circular region known as sector and segment. Class 10, Maths, Chapter 12 contains total three exercise to discuss which are given below.
Class 10 , Maths, Chapter 12, Areas related to Circles (All exercise)
Frequently Asked Questions on NCERT Solutions for class 10 maths Chapter 12 Areas related to Circles
What will I learn in NCERT Solutions for class 10 maths Chapter 12 Areas related to Circles?
Here are some of the key concepts you will learn in NCERT Solutions for Class 10 Maths Chapter 12: Areas related to Circles:
- Definition of a circle and its parts: You will learn about the various parts of a circle, such as its center, radius, diameter, and chord.
- Circumference of a circle: You will learn how to calculate the circumference of a circle using its radius or diameter.
- Arcs of a circle: You will learn about minor arcs, major arcs, and semicircles, and how to calculate their lengths and angles.
- Sector of a circle: You will learn about the sector of a circle, and how to calculate its area and perimeter.
- Theorems related to circles: You will learn about various theorems related to circles, such as the chords theorem, angles subtended by an arc theorem, and cyclic quadrilaterals theorem.
- Tangent to a circle: You will learn about tangents to a circle, and how to find the length of a tangent segment drawn from a point outside the circle.
- Construction of tangents: You will learn how to construct tangents to a circle from a point outside the circle.
- Number of tangents from a point: You will learn about the maximum number of tangents that can be drawn from a point to a circle.
By studying these concepts and practicing the exercises provided in NCERT Solutions for Class 10 Maths Chapter 12, you will gain a thorough understanding of areas related to circles, which will help you excel in your exams and in real-world applications.
What are the important formula in Class 10 Maths Chapter 12: Areas related to Circles?
There are several important formulas in Class 10 Maths Chapter 12: Areas related to Circles that you should be familiar with. Here are some of the most important ones:
- Circumference of a circle = 2πr or πd, where r is the radius and d is the diameter of the circle.
- Area of a circle = πr2, where r is the radius of the circle.
- Length of an arc of a circle = (θ/360) × 2πr, where θ is the central angle in degrees and r is the radius of the circle.
- Area of a sector of a circle = (θ/360) × πr2, where θ is the central angle in degrees and r is the radius of the circle.
- Pythagorean theorem: In a right triangle, where a and b are the lengths of the legs and c is the length of the hypotenuse, a2+b2=c2.
- Tangent to a circle: If a line is tangent to a circle at a point, then the line is perpendicular to the radius passing through that point.
- Chords theorem: If two chords intersect inside a circle, then the product of the segments of one chord is equal to the product of the segments of the other chord.
- Angles subtended by an arc theorem: If two chords in a circle intersect, then the angles formed by the chords are proportional to the arcs they subtend.
By memorizing and understanding these formulas, you can solve problems related to circles with ease and accuracy.
How are NCERT Solutions for Class 10 Maths Chapter 12 helpful in exams?
NCERT Solutions for Class 10 Maths Chapter 12: Areas related to Circles can be helpful in exams in the following ways:
- Clear understanding of concepts: NCERT Solutions provide a clear understanding of the concepts and topics covered in the chapter, making it easier for students to answer questions in exams.
- Step-by-step approach: The solutions provide a step-by-step approach to solving problems, which can help students solve similar problems in exams.
- Practice questions and answers: NCERT Solutions for Class 10 Maths Chapter 12 include a range of practice questions and answers, which can help students improve their problem-solving skills and test their understanding of the chapter.
- Exam-oriented approach: The solutions are designed keeping in mind the exam pattern and marking scheme, which can help students score better in exams.
Overall, NCERT Solutions for Class 10 Maths Chapter 12 can help students gain confidence and excel in their exams.