Chapter 10 – CIRCLES Exercise 10.1

(Q 1) Fill in the blanks :-

(i) The centre of a circle lies in interior 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.

Ans.

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

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

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

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

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

(vi) A circle divides the plane, on which it lies, in 3 (three) parts.

(Q 2) Write True or False: Give reasons for your Solutions.

(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.

Solutions: –

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

Explanation :- All points on a circle area at equal distance from a centre and this distance is called radius of circle.

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

Explanation :- There are infinite points on a circle and we can draw infinite number of chords of given length. So, circle has infinite number of equal chords.

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

Explanation :- For unequal arcs , there can be major or minor arcs. So, equal arcs on a circle can not be said as a major arc or minor arc.

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

Explanation:-Any chord whose length is twice as long as the radius of the circle always passes through the centre of the circle and thus, it is known as the diameter of the circle.

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

Explanation:- A sector is a region of a circle between the arc and the two radii of the circle.

(vi) A circle is a plane figure. (True )

Explanation:- A circle is a two dimensional figure and it can be drawn on a plane.

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