Question 1. Fill in the blanks: (i) The centre of a circle lies in _________ of the circle. (ii) A point, whose distance from the centre of a circle is greater than its radius lies in _________ of the circle. (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) interior
(v) the chord
Question 2. 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.
Solution: (i) True [∵ All points on the circle are equidistant from the centre]
(ii) False [∵ A circle can have an infinite number of equal chords.]
(iii) False [∵ Each part will be less than a semicircle.]
(iv) True [∵ Diameter = 2 x Radius]
(v) False [∵ The region between the chord and its corresponding arc is a segment.]
(vi) True [∵ A circle is drawn on a plane.]
ANGLE SUBTENDED BY A CHORD AT A POINT