NCERT Solutions for Class 10 Maths Chapter 10 Exercise 10.1 PDF

NCERT Solutions for Class 10 Maths Exercise 10.1 Chapter 10 Circles

Below is the NCERT Solutions for Class 10 Maths Exercise 10.1 Chapter 10 Circles

Solve the followings Questions.

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:

AB || CD || EF AB,CD and EF are three parallel lines where EF is the tangent to the circle. Here CD id secant(Intersecting circle at 2 points P and Q)

Benefits of Solving NCERT Solutions for Class 10 Maths Chapter 10 Exercise 10.1

• Conceptual Clarity : The solutions help students understand key concepts such as tangents, their properties, and their relationship with circles in a step-by-step manner.
• Improved Problem-Solving Skills : By practicing various types of problems, students develop logical reasoning and analytical abilities essential for geometry.
• Time Management : Solving these solutions regularly helps students improve their speed and accuracy, which is crucial during exams.
• Enhanced Visualization : Working with diagrams and proofs improves spatial understanding and enhances the ability to visualize geometrical concepts.
• Strong Foundation : This exercise lays the groundwork for understanding advanced geometrical concepts, making it easier to approach higher-level problems in future studies.