NCERT Solutions for Class 10 Maths Chapter 10 Circles

There are two exercises in class 10 Maths chapter 10. Exercises 10.2 contains all the important questions which are generally asked in school tests and board exams also. The last 5 questions given in ex. 10.2 is really very good questions to asked in exams.

Circle: A circle is the set of points in a plane which are at the same distance from a fixed point in the plane. The fixed point is called the centre of the circle and the line segment joining the centre & a point on circle is called radius.

Tangent to a circle: If a line drawn in the plane of a circle intersects the circle in one and only one point, then the line is called a tangent to the circle and the point at which the line intersect the circle is called the point of contact of the line with the circle.

There are two theorems which asked in board exams to prove.
Theorems on tangent to a circle:
(i). A tangent to a circle is perpendicular to the radius drawn from point of contact or A line drawn perpendicular to a radius at its end point on the circle is a tangent to the circle.
(ii). the tangents drawn to a circle from a point in the exterior of the circle are equal in length or the lengths of tangents drawn from an external point to a circle are equal.

There are 2 exercises in class 10 chapter 10 Circles.
In first exercise (Ex 10.1), there are only 4 questions.
In second exercise (Ex 10.2), there are in all 13 questions.
So, there are in all 17 questions in class 10 chapter 10 Circles.
There are only 3 examples (example 1, 2 and 3) in class 10 chapter 10 Circles.

In chapter 10 Circles of class 10 maths, students will study:
1) Meaning of Tangent to a Circle.
2) Meaning of Secant of the circle.
3) Point of Contact.
4) Theorem 10.1 “The tangent at any point of a circle is perpendicular to the radius through the point of contact”.
5) Number of Tangents from a Point on a Circle.
6) Length of the Tangent.
7) Theorem 10.2 “The lengths of tangents drawn from an external point to a circle are equal.”

There are only two theorems in chapter 10 Circles of 10th Math and proof of any theorem can come in exam because both the theorems are equally important from exam point of view. For exams students should prepare both the theorems.

Students need maximum 6-7 days to complete chapter 10 (Circles) of class 10th mathematics if they are giving 1 hour per day to chapter 10. Also this time depends on student’s speed, capability and many other factors.