Ex - 10.1
Question 1. Fill in the blanks
(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.
Solution
Question 1. Fill in the blanks
(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.
Solution
(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 exterior of
(ii) A point, whose distance from the centre of a circle is greater than its radius lies in exterior of
the circle. (exterior/interior)
(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 three parts.
(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 three parts.
Question 2. Write True or False: Give reasons for your answers.
(i) Line segment joining the centre of 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.
Solution
(i) True, all the points on circle are at equal distance from the centre of circle, and this equal distance
it called as radius of circle.
(ii) False, on a circle there are infinite points. So, we can draw infinite number of chords of given length. Hence, a circle has infinite number of equal chords.
(iii) False, consider three arcs of same length as AB, BC and CA. Now we may observe that for minor arc BDC. CAB is major arc. So AB, BC and CA are minor arcs of circle.
(iv) True, let AB be a chord which is twice as long as its radius. In this situation our chord will be passing through centre of circle. So it will be the diameter of circle.
(v) False, sector is the region between an arc and two radii joining the centre to the end points of the arc as in the given figure OAB is the sector of circle.
(vi) True, A circle is a two dimensional figure and it can also be referred as plane figure.
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