# NCERT Solutions for Class 10 Maths Chapter 10 Circles Ex 10.1

These NCERT Solutions for Class 10 Maths Chapter 10 Circles Ex 10.1 Questions and Answers are prepared by our highly skilled subject experts.

## NCERT Solutions for Class 10 Maths Chapter 10 Circles Exercise 10.1

Question 1.
How many tangents can a circle have?
Solution:
There can be infinitely many tangents to a circle.

Question 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 ……….. .
Solution:
(i) One
(ii) Secant
(iii) Two
(iv) Point of contact.

Question 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) $$\sqrt{199}$$ cm
Solution:
We have given that PQ is a tangent of a circle whose centre is O are radius 5 cm. Length of OQ = 12 cm.

We know that, the tangent at any point of a circle is perpendicular to the radius through the point of contact.
OQ = 12 cm
∴ ∠OPQ = 90°
[The tangent to a circle is perpendicular to the radius through the point of contact]
PQ2 = OQ2 – OP2 [By Pythagoras theorem]
PQ2 = 122 – 52 = 144 – 25 = 199
∴ PQ = $$\sqrt{199}$$ cm.
Hence correct option is (d).

Question 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.
Solution:

PQ is a tangent and LM a secant.

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