Circles : Exercise 10.1 (Mathematics NCERT Class 10th)

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 ______.
Sol.         (i) exactly one
               (ii) secant
               (iii) two
               (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) \sqrt {119} cm
Sol.         (D). Because,
                PQ = \sqrt {O{Q^2} - O{P^2}} = \sqrt {{{12}^2} - {5^2}} = \sqrt {144 - 25}
                 = \sqrt {119} \,cm

Q.4      Draw a circle and two lines parallel to a given line such that one is tangent and the other, a secant to the circle.
Sol.        The required figure is as under :
               Here \ell is the given line and a circle with centre O is drawn.
               Line PT is drawn || to line \ell .
               PT is the tangent to the circle.
               AB is drawn || to line \ell and is the secant.



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