Gujarat Board GSEB Solutions Class 10 Maths Chapter 10 Circles Ex 10.1 Textbook Questions and Answers.

## Gujarat Board Textbook Solutions Class 10 Maths Chapter 10 Circles Ex 10.1

Question 1.

How many tangents can a circle have?

Solution:

Infinite many tangents. As there are infinitely many points on a circle and all the points can have its tangent.

Question 2.

Fill in the blanks:

- A tangent to a circle intersects it in …………. point(s).
- A line intersecting a circle in two points is called a ……….
- A circle may have ……….. parallel tangents at the most.
- The common point of a tangent to a circle and the circle is called ……….

Solution:

- one
- secant
- two
- point of contact

Question 3.

A tangent PQ at a point P of a circle of radius 5 cm meets a line through the center O at a point Q so that OQ = 12 cm. Length PQ is

(a) 12 cm

(b) 13cm

(c) 8.5 cm

(d) 19 cm

Solution:

(d)

From figure,

∠OPQ = 900 (Theorem 10.1)

∴ ΔOPQ is a right-angled triangle.

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 tangent and other, a secant to the circle.

Solution:

1. Draw a circle with center O.

2. Draw a line AB passing through O.

3. Draw a perpendicular bisector CD of AB.

4. From D, draw ∠ODF = 90°.

5. Take a point G on OD and draw ∠OGY = 90°.

∴ XY is a secant and EF is a tangent and AB || XY || EF.