Well-designed AP 10th Class Maths Solutions Chapter 10 Circles Exercise 10.1 offers step-by-step explanations to help students understand problem-solving strategies.

## Circles Class 10 Exercise 10.1 Solutions – 10th Class Maths 10.1 Exercise Solutions

Question 1.

How many tangents can a circle have?

Solution:

Number of tangents can be drawn to a circle are infinite (many).

Tangents to the given circle are k, l, m, n, P, q, ……….

Question 2.

Fill in the blanks :

i) A tangent to a circle intersects it in ________ point (s).

Answer:

only one

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

Answer:

secant of the circle.

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

Answer:

two

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

Answer:

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) \(\sqrt{119}\) cm.

Solution:

D) \(\sqrt{119}\) cm.

Given radius OP = 5 cm

OQ = 12 cm

In ∆POQ, ∠OPQ = 90°

Angle at the point of contact with the radius by the tangent by using Pythagoras theorem,

OP^{2} + PQ^{2} = OQ^{2}

5^{2} + PQ^{2} = 12^{2}

PQ^{2} = 144 – 25 = 119

∴ PQ = \(\sqrt{119}\) 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.

Steps:

1) Draw a circle with some radius.

2) Draw a chord of the circle.

3) Draw a line parallel to the chord intersecting the circle at two distinct points.

4) This is secant of the circle (l).

5) Draw another line parallel to the chord, just touching the circle at one point (M). This is a tangent of the circle.