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.
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.
Related Questions
Draw a rough sketch of a quadrilateral KLMN. State:
(i) two pairs of opposite sides
(ii) two pairs of opposite angles
(iii) two pairs of adjacent sides
(iv) two pairs of adjacent angles
In the adjoining figure, identify:
(i) the centre of the circle
(ii) three radii
(iii) a diameter
(iv) a chord
(v) two points in the interior
(vi) a point in the exterior
(vii) a sector
(viii) a segment.
Fill in the following blanks:
(i) There is exactly one line passing through ….. distinct points in a plane.
(ii) Two different lines in a plane either ….. at exactly one point or are parallel.
(iii) The curves which have different beginning and end points are called ….. curves.
(iv) A curve which does not cross itself at any point is called a ….. curve.
(v) A simple closed curve made up entirely of line segments is called a …. .
(vi) A quadrilateral has ….. diagonals.
(vii) A line segment has a ….. length.
Fill in the blanks with correct word(s) to make the statement true:
(i) Radius of a circle is one-half of its …..
(ii) A radius of a circle is a line segment with one end point at ….. and the other end-point on …..
(iii) A chord of a circle is a line segment with its end points ….
(iv) A diameter of a circle is a chord that ….. the centre of the circle.
(v) All radii of a circle are …..