NCERT Solutions Maths Class 10 Exercise 10.1

# NCERT Solutions Maths Class 10 Exercise 10.1

## Maths Class 10 Exercise 10.1

1. How many tangents can a circle have?

Answer: Since there are infinitely many points on the circumference of a circle and at each point we can draw a unique tangent, therefore, a circle can have infinitely many tangents.

2. Fill in the blanks:

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

(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) 119 cm

Solution: (D) Since, PQ is the tangent and OP is the radius through the point of contact.

Therefore, OPQ = 90°

[Since, the tangent at any point of a circle is perpendicular to the radius through the point of contact.]

In right-angled ∆OPQ, we have

OQ2 = OP2 + PQ2                [By Pythagoras theorem]

(12)2 = (5)2 + (PQ)2

144 = 25 + PQ2

PQ2 = 144 – 25 = 119

PQ = √119 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.

Solution: