Q.1. How many tangents can a circle have?
Sol. A circle can have an infinite number of tangents.
Q.2. Fill in the blanks
(i) A tangent to a circle intersects it in .......... point(s).
(ii) A line intersecting a circle in two points is called a ...........
(iii) A circle can have .......... parallel tangents at the most.
(iv) The common point of a tangent to a circle and the circle is called ...........
(i) exactly one
(iv) point of contact.
Q.3. A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length of PQ is:
(a) 12 cm
(b) 13 cm
(c) 8.5 cm
(d) √199 cm
Radius of the circle = 5 cm
► OQ = 12 cm
► ∠OPQ = 900
[The tangent to a circle is perpendicular to the radius through the point of contact]
► PQ2 = OQ2 - OP2 [By Pythagoras theorem]
► PQ2 = 122 - 52 = 144 - 25 = 199
► PQ = √199 cm
Hence correct option is (d)
Q.4. Draw a circle and two lines parallel to a given line such that one is a tangent and the other a secant to the circle.
Sol. A line 'm' is parallel to the given line 'n' and a line 'l' which is secant is parallel to the given line 'n'.