Chapter 10 – Circles (Ex – 10.1)

Circles

Question 1.
How many tangents can a circle have?

Solution:
A circle can have an infinite number of tangents.

Question 2.
Fill in the blanks :

1. A tangent to a circle intersects it in ________ point(s).
2. A line intersecting a circle in two points is called a ________.
3. A circle can have ________ parallel tangents at the most.
4. The common point of a tangent to a circle and the circle is called ________.

Solution:

1. exactly one
2. secant
3. two
4. 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 of PQ is :
(A) 12 cm
(B) 13 cm
(C) 8.5 cm
(D) √119 cm

Solution:
(D) Because,
PQ = √(OQ²−OP²)
= √(12²−5²) cm
= √(144−25) cm
= √119 cm.

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:
The required figure is given below.
Here l is the given line and a circle with centre O is drawn.
Line PT is drawn || to line l.
PT is the tangent to the circle.
AB is drawn || to line l and is the secant.