Page 161 - Math Skill - 5

Geometry 159

Circle
A circle is a closed curve in which each point on its boundary is at the same
distance from a fixed point in the circle. This fixed point is known as the centre of O
the circle. In the figure, point O is the centre of circle.

Radius of a Circle

A The line segment joining the centre of the circle to any point on the circle is
B called the radius of the circle.

O C In the given figure, O is the centre of the circle and OA, OB, OC and OD are
D the radii of the circle.

Diameter of a Circle

The line segment having its end points on the circle and passing through the centre is called its
diameter. Fact-o-meter
In the given figure, O is the centre and AB is the diameter. � In singular, we write as

AB = OA + OB = OA + OA ‘radius’ and in plural, we
B
= 2 OA write as ‘radii’.
= 2 × radius O � The lengths of all the
A radii of a circle are equal.

Diameter = 2 × radius (OA = OB = radius of circle)

Let’s Attempt

Example 1: Find the diameter of a circle whose radius is 4 cm.
Solution: Radius = 4 cm Fact-o-meter
Diameter = 2 × Radius = 2 × 4 cm = 8 cm We can draw infinite

Hence, the diameter of the given circle is 8 cm. number of radii and
Example 2: Find the radius of a circle whose diameter is 9 cm. diameters in a circle.

Solution: Diameter = 9 cm
1 1
Radius = × Diameter = × 9 cm = 4.5 cm
2 2
Hence, the radius of the given circle is 4.5 cm.

Interior and Exterior of Circle

The region of plane enclosed by circle is called interior of circle. The region of plane outside the
circle is called exterior of circle. In the given figure:

™ Points A, B and O lie in the interior of circle. A

™ Points C and D lie on the circle. E B O F
C
™ Points E and F lie in the exterior of circle. D