## Exercise 18

Question 1:

Take a point O on your notebook and draw circles of radii 4 cm, 5.3 cm and 6.3 cm, each having the same centre O.

Solution:

This is the required diagram as asked in the question.

Question 2:

Draw a circle with centre C and radius 4.5 cm. Mark points P, Q, R such that P lies in the interior of the circle, Q lies on the circle, and R lies in the exterior of the circle.

Solution:

This is the required diagram as asked in the question.

Question 3:

Draw a circle with centre O and radius 4 cm. Draw a chord AB of the circle. Indicate by marking points X and Y, the minor arc AXB and the major arc AYB of the circle.

Solution:

This is the required diagram as asked in the question.

Question 4:

Which of the following statements are true and which are false?

(i) Each radius of a circle is also a chord of the circle.

(ii) Each diameter of a circle is also a chord of the circle.

(iii) The centre of a circle bisects each chord of the circle.

(iv) A secant of a circle is a segment having its end points on the circle.

(v) A chord of a circle is a segment having its end points on the circle.

Solution:

(i) False

Diameter of a circle is a chord of the circle, not radius.

(ii) True

It is the longest chord of the circle.

(iii) False

A perpendicular drawn from the centre of the circle to the chord, bisects the chord.

(iv) False

It is a line passing through the circle that intersects the circle at two points.

(v) True

Question 5:

Draw a circle with centre O and radius 3.7 cm. Draw a sector having the angle 72^{o}.

Solution:

Therefore, the required arc is arc OACB.

Question 6:

Fill in the blanks by using <, >, = or \(leq\)

(i) OP _____ OQ, where O is the centre of the circle, P lies on the circle and Q is in the interior of the circle.

(ii) OP _____ OR, where O is the centre of the circle, P lies on the circle and R lies in the exterior of the circle.

(iii) Major arc _______ minor arc of the circle.

(iv) Major arc _______ semi circumference of the circle.

Solution:

(i) >

(ii) <

(iii) >

(iv) >

This is because the major arc covers more than half of the circumference of the circle.

Question 7:

Fill in the blanks:

(i) A diameter of a circle is a chord that _________ the centre.

(ii) A radius of a circle is a line segment with one end point ________ and the other end point __________ .

(iii) If we join any two points of a circle by a line segment, we obtain a _________ of a circle.

(iv) Any part of a circle is called an ________ of an circle.

(v) The figure bounded by an arc and the two radii joining the end points of the arc with the centre is called a __________ of the circle.

Solution:

(i) passes through

(ii) on the circle, at the centre of the circle

(iii) chord

(iv) arc

(v) sector