Explain the following:

(i) Circle
(ii) Radius
(iii) Centre
(iv) Diameter
(v) Chord
(vi) Interior of a circle

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Solution

(i) A circle is a set of all those points in a plane, whose distance from a fixed point remains constant.
(ii) Radius of a circle is a line segment with one end at its centre and the other end on the circle. (It is the constant distance between all the points on the circle and its centre.)
(iii) The centre of a circle is that fixed point from which all points remain at a constant distance.
(iv) Diameter of a circle is a line segment passing through the centre of a circle, and having its end points on the circle.
(v) A chord of a circle is a line segment with its end points lying on the circle.
(vi) Interior of a circle is a set of all those points which lie inside the circle.

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(i) The centre of a circle lies in __________ of the circle. (exterior/ interior)

(ii) A point, whose distance from the centre of a circle is greater than its radius lies in __________ of the circle. (exterior/ interior)

(iii) The longest chord of a circle is a __________ of the circle.

(iv) An arc is a __________ when its ends are the ends of a diameter.

(v) Segment of a circle is the region between an arc and __________ of the circle.

(vi) A circle divides the plane, on which it lies, in __________ parts.

2 \times

Write True or False: Give reasons for your answers.

(i) Line segment joining the centre to any point on the circle is a radius of the circle.

(ii) A circle has only finite number of equal chords.

(iii) If a circle is divided into three equal arcs, each is a major arc.

(iv) A chord of a circle, which is twice as long as its radius, is a diameter of the circle.

(v) Sector is the region between the chord and its corresponding arc.

(vi) A circle is a plane figure.

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