Page 217 - ICSE Math 8

20 Circles

Key Concepts

• Circle • Angles in a Semicircle
• Angle Subtended by an Arc

Circle

A circle is simple closed curve formed by a set of points that are equidistant from a
fixed point. A circle can also be defined as the path traced by a point which moves in O
such a way that its distance from a fixed point is always same. The fixed point is called radius P
the centre of the circle and the fixed distance is known as the radius of the circle. In
the adjoining figure, O is the centre and OP is the radius.

Chord
The line segment joining any two points on a circle is called a chord. In the adjoining L S
figure, KL is a chord of the circle with centre at O. Infinite number of chords can be
drawn for a circle. chord diameter O P

Diameter K radius
Diameter is a chord passing through the centre of the circle. In the adjoining figure, R
RS is the diameter of the circle.
Diameter is the longest chord of a circle. Maths Info
RS = RO + OS = 2RO ( RO = OS = radius) A chord can be drawn in a circle only

∴ Diameter = 2 × Radius if its length is less than or equal to the
diameter of the circle.
Circumference
The length of the boundary of a circle is called its circumference. It is also called the perimeter of the circle.

Interior and exterior of a circle
The region inside a circle is known as its interior and the region outside a circle is known B
as its exterior. Interior of a circle can also be defined as the set of all the points which lie
inside a circle (point A). The set of all the points which lie outside a circle is known as O
exterior (point C). A
A point whose distance from the centre of the circle is equal to the radius, is said to be
on the circumference of the circle. In the adjoining figure, OB = radius. Therefore, B lies C
on the circumference of the circle. All the points that lie inside and on the circle forms
the circular region.
Example 1: O is a fixed point in a plane and point A moves at a fixed distance of 5 cm from O. State:
(a) the figure formed (b) the length of radius of the figure
(c) the length of the diameter of the figure

Solution: (a) The figure formed is a circle with centre O. (b) Radius of circle = OA = 5 cm
(c) Diameter = 2 × Radius = 2 × 5 = 10 cm

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