Circles - Solutions
CBSE Class–10 Mathematics
NCERT solution
Chapter - 10
Circles - Exercise 10.1
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.
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 exactly 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.
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
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. 