RD Sharma Class 11 Chapter 24 Solutions (The Circle)
RD Sharma Solutions for Class 11 Maths Chapter 24 will give you an exhaustive knowledge of all the theorems related to circles. You will be able to master all the different ways that any question on circles can be presented to you in any exam. The various topics discussed in this chapter make you well-versed with most common equations of a circle with many special cases along with introducing the radius, diameter, tangent, the distance between 2 points on a circle and how tangent and diameter are related to each other.
RD Sharma Class 11 Solutions for Maths Chapter 24 has a total of 101 and 5 exercises. Some questions have very short answers and are objective type where you have to choose one right answer from multiple choices. Some of the questions are complex that require you to employ many concepts of a circle in solving them. This chapter will prepare you well on the topic of circles for your CBSE exams.
Maths experts at Instasolv have given a very lucid and simple way of solving the problems in this chapter with the help of RD Sharma Class 11 Solutions for Maths Chapter 24 – The Circle. With tips on how to manage your time better, you should be able to handle the stressful examination environment easily.
Topics Covered in RD Sharma Solutions for Class 11 Maths Chapter 24 – The Circle
- Rule of the circle – For a circle, any point on its circumference is at the same distance from the centre of the circle.
- Radius – The distance from the centre of the circle to its circumference is called its radius.
- Equation of a Unit Circle with the centre point (0,0) – A circle whose centre is (0,0) is called a unit circle. If it has a point (a,b) on its circumference and its radius is r then based on Pythagoras’ theorem, the following holds: a² + b² = r²
- Standard equation of a circle OR the distance formula – The above formula for a circle can be generalized by considering centre at (c1, c2) and (p1, p2) is the coordinates of a point on the circumference and its radius is r, so the standard equation can be stated as: (p1 – c1)² + (p2 – c2)² = r²
- General equation of circle – The standard equation of the circle can be generalized by considering that centre of a circle is (-c1, -c2) and (p1, p2) is the coordinates of a point on the circumference and its radius is r, so the general equation can be stated as: p1² + p2² + 2 (c1 * p1) + 2 (c2 * p2) + k = 0, where k is a constant and k = c1² + c2² – r²
- Diameter of a Circle – A line segment that crosses through the centre of a circle with its endpoints on the circumference of the circle is called the diameter of a circle. For a given circle, all its diameters are of the same length. The length of the diameter is twice the length of its radius. There are many equations around the diameter:
- If the radius is known then d = 2 * r
- If the circumference is known then d = C / π
- If the area of the circle is known then d = √(4* area) / π
Here d = diameter, r = radius, C = circumference, π = pi = 3.142
Concepts around the diameter of a circle
- Chord – Any line which joins 2 points on a circle is called a chord. Diameter is the longest chord in a circle.
- Thales’ theorem – If a triangle is drawn from diameter to any point on the circumference of a circle, it will always be a right angle (90º)
- Isosceles triangle – If 2 radii and a chord are joined then we get an isosceles triangle which is a triangle where at least 2 sides have the same length.
- Bisecting a chord – if a perpendicular line is dropped from the centre of a circle to any of its chord, it will divide the chord’s length into 2 halves.
- Tangent of a circle – A line that touches the circumference of a circle at just one point is called its tangent. The point of tangency is the point where a tangent comes in contact with the circle. A line drawn from the centre of a circle to the point of tangency is at 90º with the tangent at that point.
Discussion of Exercises of RD Sharma Solutions for Class 11 Maths Chapter 24
- The questions in the first exercise of RD Sharma Class 11 maths chapter 24 are based on finding the circle’s equation where you will be given the centre and radius of the circle. It has 31 questions.
- The second set of exercises gives you ample practice on general equations of a circle with various methods of applying them. It has 24 questions.
- The third set is centred around concepts on the diameter and chord of a circle. It has 12 questions.
- The fourth set has questions that have very short answers based on the area of a circle, diameter and general equation of a circle. It has 9 questions.
- The fifth set is the MCQ section with objective questions on the equation of the circle. It has 25 questions.
Benefits of RD Sharma Solutions for Chapter 24 by Instasolv
Instasolv has made it very easy, in clear steps, on how to approach any complex problem related to a circle. The RD Sharma Solutions for Class 11 Chapter 24 from Instasolv come without any cost and are a great way of learning time management during exams. The solutions are arranged in a manner which will give you immense learning on all the concepts around a circle. They will give you a strong base to secure good marks in any exam whether it be CBSE, JEE or NEET.