NCERT Solutions for Class 10 Maths Chapter 10 Circles
In our previous classes, we have learnt that a circle is a closed shape with a collection of points in a plane which are at a specific distance ( called radius) from a fixed point (called centre). We have also studied important terms related to the circle like segment, arc, sector, chord etc. In this chapter, there are two exercises with 17 questions in them. The NCERT Solutions for Class 10 Maths Chapter 10 Circles are solved by our maths experts to help students in their preparation of CBSE Class 10 Board exam. These NCERT solutions are the stepbystep explanation of each and every question of class 10 NCERT textbook.
In this chapter, we will study the different conditions that arise when a line and a circle are given in a plane. And to solve these type of situations we will learn the concept of the tangent to a circle and the number of tangents from a point on a circle in NCERT Class 10 Maths Chapter 10 Circles. This chapter has fundamental concepts which are important for students in their future studies. This chapter introduces some complex and important terms like tangents, tangents to a circle, number of tangents from a point on a circle. NCERT Class 10 Maths Chapter 10 Circles is a very interesting chapter due to the involvement of geometrical calculations and the diagrams.
The two important theorems of Chapter 10 Circles are
Theorem 10.1: The tangent at any point of a circle is perpendicular to the radius of the circle through the point of contact.
Proof: Assume O is the centre of the circle and XY is the tangent to the circle at point P. And we need to prove that OP is perpendicular to the XY.
Take point Q on XY other than point P and join OQ. The point Q lies outside the circle. Therefore, OQ is longer than the radius of the circle OP.
Except for point P, this happens for every time on the line XY. OP is the shortest distances of the point O to the points of line XY. So that's why OP is perpendicular to the line XY.
Theorem 10.2: The lengths of tangents drawn from an external point to a circle are equal.
Proof: Assume O is the centre of the circle, a point P lying outside a circle and two tangents PQ and PR on the circle from point P. We need to prove .
For this, we join OP, OQ and OR. Then and are right angles, because these two are angles between the tangents and radii, and according to Theorem 10.1, they are right angles. Now in right triangles ORP and OQP.
10.2 Tangent to a Circle
10.3 Number of Tangents from a Point on a Circle
10.4 Summary
The complete Solutions of NCERT Class 10 Mathematics Chapter 10 is provided below:
Chapter No. 
Chapter Name 
Chapter 1 

Chapter 2 

Chapter 3 

Chapter 4 

Chapter 5 

Chapter 6 

Chapter 7 

Chapter 8 

Chapter 9 

Chapter 11 

Chapter 12 

Chapter 13 

Chapter 14 

Chapter 15 
3. If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of , then POA is equal to
(A) 50°
(B) 60°
(C) 70°
(D) 80°
10. Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the linesegment joining the points of contact at the centre.
2. Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it whose sides are 2/3 of the corresponding sides of the first triangle.