NCERT Class 10 Maths Chapter 10 Circles Exercise 10.1

Chapter 10 Circles Exercise 10.1

Question 1: How many tangents can a circle have?
Answer: There are infinitely many tangents that a circle can have.

Question 2: Fill in the blanks:
(i) A tangent to a circle intersects it in  1  point (s).
(ii) A line intersecting a circle in two points is called a secant.
(iii) A circle can have  2  parallel tangents at the most.
(iv) The common point of a tangent to a circle and the circle is called 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) 119 cm
Answer:
Given:
Radius of the circle = 5 cm
OQ = 12 cm
∠ OPQ = 90° (as the tangent to a circle is perpendicular to the radius through the point of contact)

PQ² = OQ² - OP²        (by Pythagoras theorem)
= PQ² = (12)² - (5)²
= PQ = √(144 - 25)
= PQ = √199

Hence, the correct option is d) √119.

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.
Answer:

Here in the above figure, AB is the given line. CD is the tangent to the given circle, which intersects the circle at Q, is parallel to AB. EF is a secant parallel to AB.