Circles Exercise 10.1

NCERT solutions for Maths Circles 

NCERT Solutions for Class 10 Maths Circles

1. How many tangents can a circle have?

Ans. 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.

NCERT Solutions for Class 10 Maths Exercise 10.1

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 _______________.

Ans. (i) A tangent to a circle intersects it in one point.

(ii) A line intersecting a circle in two points is called a secant.

(iii) A circle can have two parallel tangents at the most.

(iv) The common point of a tangent to a circle and the circle is called point of contact.

NCERT Solutions for Class 10 Maths Exercise 10.1

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) cm

Ans. (D) PQ is the tangent and OP is the radius through the point of contact.

OPQ = [The tangent at any point of a circle is to the radius through the point of contact]

In right triangle OPQ,

OQ² = OP² + PQ² [By Pythagoras theorem]

= 144 – 25 = 119

PQ = cm

NCERT Solutions for Class 10 Maths Exercise 10.1

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.

Ans.