Fill in the blanks:
(i) A chord of a circle is a line segment with its end points ... .
(ii) A diameter of a circle is a chord that ... the centre of circle.
(iii) A line meets a circle atmost in ... points.
(iv) One-half of the whole arc of a circle is called a ... .
(v) The angle subtended by an arc of a circle at the centre of the circle is called the ... by the arc.
(vi) A line which meets a circle in one and only one point is called a ... to the circle.
(vii) The tangent at any point of a circle and the radius through that point are ... to each other.
(viii) From a point outside the circle, ... tangents can be drawn to the circle.
(ix) The measure of an angle in a semicircle is ... .
Answer
(i) A chord of a circle is a line segment with its end points on the circle.
(ii) A diameter of a circle is a chord that passes through the centre of circle.
(iii) A line meets a circle atmost in two points.
(iv) One-half of the whole arc of a circle is called a semicircle.
(v) The angle subtended by an arc of a circle at the centre of the circle is called the angle subtended by the arc.
(vi) A line which meets a circle in one and only one point is called a tangent to the circle.
(vii) The tangent at any point of a circle and the radius through that point are perpendicular to each other.
(viii) From a point outside the circle, two tangents can be drawn to the circle.
(ix) The measure of an angle in a semicircle is 90°.
State whether the following statements are true (T) or false (F):
(i) A line segment with its end-points lying on a circle is called a radius of the circle.
(ii) Diameter is the longest chord of the circle.
(iii) The end-points of a diameter of a circle divide the circle into two parts; each part is called a semicircle.
(iv) A diameter of a circle divides the circular region into two parts; each part is called a semicircular region.
(v) The diameters of a circle are concurrent. The centre of the circle is the point common to all diameters.
(vi) Every circle has unique centre and it lies inside the circle.
(vii) Every circle has unique diameter.
(viii) From a given point in the exterior of a circle, two tangents can be drawn to it and these two tangents are equal in length.
Answer
(i) A line segment with its end-points lying on a circle is called a chord of the circle and not a radius of the circle.
Hence, the given statement is false.
(ii) The longest chord of a circle is the one which passes through the centre of the circle and it is called the diameter.
Hence, the given statement is true.
(iii) The end-points of a diameter of a circle divide the circle into two equal arcs and each of these arcs is called a semicircle.
Hence, the given statement is true.
(iv) A diameter of a circle divides the circular region into two equal parts and each of these parts is called a semicircular region.
Hence, the given statement is true.
(v) Every diameter of a circle passes through its centre, so all the diameters of a circle are concurrent and the centre is the point common to all of them.
Hence, the given statement is true.
(vi) A circle has one and only one centre and this centre always lies in the interior of the circle.
Hence, the given statement is true.
(vii) An infinite number of diameters can be drawn in a circle as every chord passing through the centre is a diameter.
Hence, the given statement is false.
(viii) From a point lying in the exterior of a circle, exactly two tangents can be drawn to the circle and these two tangents are equal in length.
Hence, the given statement is true.