NCERT Class 10 Maths Chapter 8 Circles, introduces important concepts related to tangents and their properties. Exercise 8.1 focuses on understanding the fundamental idea of a tangent to a circle and how it behaves with respect to the radius.
This concept is a core part of the Class 10 Maths syllabus and forms the base for many geometry problems.
In this exercise, you will learn that a tangent at any point on a circle is always perpendicular to the radius at the point of contact. These NCERT Solutions for Exercise 8.1 provide clear, step-by-step explanations that will help you through each problem.
NCERT Solutions for Class 10 Maths Chapter 8 Exercise 8.1
1. How many tangents can a circle have?
Answer:
A circle can have infinitely many tangents since there are infinitely many points on the circumference of the circle and at each point of it, it has a unique tangent.
2. Fill in the blanks:
(i) A tangent to a circle intersects it in _______________ point(s).
(ii) A line intersecting a circle in two points is called a _______________.
(iii) A circle can have _______________ parallel tangents at the most.
(iv) The common point of a tangent to a circle and the circle is called _______________.
Answer:
(i) one
(ii) secant
(iii) two
(iv) point of contact
3. A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm.
Length PQ is: (A) 12 cm (B) 13 cm (C) 8.5 cm (D) √119 cm
Answer:
(D)

We know that the line drawn from the centre of the circle to the tangent is perpendicular to the tangent.
∴OP ⊥ PQ By applying Pythagoras theorem in ΔOPQ,

4. Draw a circle and two lines parallel to a given line such that one is a tangent and the other, a secant to the circle.
Answer:
.png)
AB || CD || EF AB, CD and EF are three parallel lines where EF is the tangent to the circle. Here CD is secant (Intersecting circle at 2 points P and Q)
How to Score Better in Class 10 Maths Exam?
Scoring well in Class 10 Maths requires clear concepts, regular practice, and a focus on accuracy and answer presentation. To score better, you should:
Focus on understanding concepts in Class 10 Maths instead of memorising steps, as this helps in solving application-based questions.
Focus on difficult topics from the Class 10 Maths syllabus instead of skipping them to avoid losing marks.
Regular revision of PW Class 10 Maths MIQs helps avoid calculation mistakes in exams.
Solve all CBSE Class 10 NCERT questions multiple times to strengthen your basics and improve accuracy.
Practising CBSE Class 10 Previous Year Question Papers (PYQs) helps you understand question patterns and important topics.