Math՚s: Circle: Measurement of Circumference and Some Important Rules on Circles (For CBSE, ICSE, IAS, NET, NRA 2022)

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Measurement of Circumference

The ratio of the circumference of a circle to its diameter is always a constant. This constant is universally denoted by Greek letter Thus, the circumference of a circle is calculated as-

Where stands for the diameter of the circle and the approximate value of

Example- Find the circumference of a circle whose radius is cm.

Solution-

cm

Some Important Rules on Circles

Two arcs of a circle are congruent if and only if the angles subtended by them at the center are equal. Thus, if , then

Some Important Rules on Circles

Two arcs of a circle are congruent if and only if their corresponding chords are equal. Thus, if , then

Two Arcs of a Circle

Equal chords of a circle subtend equal angles at the center and conversely if the angles subtended by the chords at the center of a circle are equal, then the chords are equal. Thus if , then or vice versa.

Equal Angles at the Centre

The perpendicular drawn from the center of a circle to a chord bisects the chord. Conversely, the line joining the center of a circle to the mid-point of a chord is perpendicular to the chord. Thus if , then or vice versa.

Chord Bisects

There is one and only one circle passing through three non-collinear points.

Non-Collinear Points

Equal chords of a circle are equidistant from the center or chords, that are equidistant from the center of a circle, are equal. Thus, if then or vice versa.

Equal Chords of a Circle

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