## RS Aggarwal Class 6 Math Eighteenth Chapter Circles Exercise 18 Solution

## EXERCISE 18

**CIRCLE** – *A circle is the collection of all those points in a plane whose distance from a fixed point remains constant.*

**INTERIOR CIRCLE** – *The part of the plane, consisting of those points which are less than the radius of the circle is called the interior of the circle.*

**EXTERIOR CIRCLE** – *The part of the plane, consisting of those points which are greater than the radius of the circle is called the exterior of the circle.*

**DIAMETER OF A CIRCLE** – *A line segment passing through the centre of a circle and having its end points on the circle is called a diameter of the circle.*

**CHORD OF A CIRCLE** – *A line segment with its end points lying on a circle is called a chord of the circle.*

**SECANT OF A CIRCLE** – *A line passing through a circle and intersecting the circle at two points is called a secant of the circle.*

**CIRCUMFERENCE OF A CIRCLE** – *The perimeter of a circle is called circumference.*

**SEGMENTS OF A CIRCLE** – *A chord of a circle divides the circular region into two parts. Each part is called segment of the circle.*

**SEMICIRCLE** – *The end points of a diameter of a circle divide the circle into two equal parts; each part is called a semicircle.*

**ARC **– *Any part of a circle is called arc of a circle.*

**SECTOR OA A CIRCLE** – *The area bounded by an arc and the two radii joining the end points of the arc with the centre is called a sector.*

**CONCENTRIC CIRCLES** – *Two or more circles with the same centre are called concentric circle. *

**(1) Take a point O on your notebook and draw circles of radii 4cm, 5.3 cm and 6.2 cm, each having the same centre O.**

This is the required diagram.

**(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.**

This is the required diagram.

**(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.**

This is the required diagram.

**(4) Which of the following statements are true and false?**

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

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

(iii) The center of a circle bisects each chord of the circle. = False

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

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

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

Therefore, the required arc is arc OACB.

**(6) fill in the blanks by using <, >, = or ****.**

(i) OP > OQ, where O is 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 center 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.

**(7) Fill in the blanks:**

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

(ii) A radius of a circle is a line segment with one end point __at the centre__ and the other end point __on the circle__.

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

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

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