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Circles

Ferris wheel Examples of circles in real life Clockwise
Hoop, Bangles, Wheel, Basketball ring

Introduction

Circle: A circle is the locus of a point which moves in a plane in such a way that its distance from a given fixed point is always constant. The fixed point is called the center and the constant distance is called the radius (plural: radii) of the circle. A circle is usually named by its center point. The figure below shows circle O, which can be written as ⊙O but is rarely used.

Note: An important point to note is that the line segment joining the center and any point on the circle is called its radius. That is, radius is used in two senses: (i) in the sense of a line segment and (ii) in the sense of its length.

Chord

A line segment joining any two points on the circumference of a circle is called a chord of the circle. In the following figure, in circle O, line segments MN, XZ, PY and AB are the chords. Here, AB is the longest chord which passes through the center. This is called the diameter of the circle.

Note:
i) The line extension of a chord is known as secant line or just secant.
ii) Two chords are equidistant from the center only if their lengths are equal.
iii) When the chord ends are joined at the center of the circle, it forms an isosceles triangle.

Do not smoke sign No Smoking! A real life example of a diameter can be found in a "No Smoking" sign. The line crossing the image of the cigarette passes through the center of the circle. Hence, AB is the diameter.
Diameter

A chord that passes through the center of a circle is called a diameter. In Fig. (i), the chord AB passes through the center O. Therefore, AB is a diameter of the circle O.

Properties of a diameter: (i) A diameter is the largest chord of a circle; (ii) All diameters of a circle are equal in length (in Fig. (ii) AB = CD); (iii) Half of the diameter is equal to the radius of a circle (in Fig. (ii) OB = AB/2); (iv) The diameter divides a circle into two equal parts, each part being a semi-circle. In Fig. (ii), the diameter AB divides circle O into two semi-circles called semi-circle ACB and semi-circle ADB.

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