Mathematics
State whether the following statements are true (T) or false (F):
(i) Every diameter of a circle is also a chord.
(ii) Every chord of a circle is also a diameter.
(iii) Two diameters of a circle will necessarily intersect.
(iv) The centre of the circle is always in its interior.
Geometrical Concepts
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Answer
(i) True
Reason — A chord is a line segment joining any two points on the circle. A diameter is a chord that passes through the centre of the circle. So every diameter is also a chord.
(ii) False
Reason — Only those chords which pass through the centre of the circle are called diameters. A chord that does not pass through the centre is not a diameter.
(iii) True
Reason — Every diameter of a circle passes through the centre. So any two diameters of a circle will always meet (intersect) at the centre of the circle.
(iv) True
Reason — The centre of a circle is the fixed point from which the distance to every point on the circle is equal to the radius. Since this distance is zero (which is less than the radius), the centre always lies in the interior of the circle.
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