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Q.

Which of the following statements is correct?

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a

The centre of a circle lies in the exterior of the circle.

b

Two diameters of a circle never intersect at the centre.

c

Only one chord can be drawn passing through the centre of a circle.

d

From a point on a circle, an infinite number of chords can be drawn.

answer is D.

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Detailed Solution

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Question Image

The region enclosed by a closed curve is called the interior region, whereas the region outside the closed curve is called the exterior region. The centre of a circle always lies in the interior of the circle. Here, centre O lies in the interior of the circle.

Question Image

A chord is a line segment joining any two points on a circle. There are infinite numbers of points on a circle. Thus, from a point on a circle, an infinite number of chords can be drawn. Here, AB, AC, AD, and AE are chords drawn from point A. Such chords can be drawn in infinite numbers.

Question Image

The diameter is a chord passing through the centre of the circle. Therefore, any two diameters will always intersect at the centre. Here, AB and CD are the diameters of the circle, which intersect at the centre O.

Also, as we can draw infinite numbers of diameters of a circle, we can also draw infinite numbers of chords passing through the centre of a circle.

Thus, we can say that 'From a point on a circle, an infinite number of chords can be drawn.' is the correct statement.

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