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Practice each question, then open the answer or worked solution.
How many tangents can a circle have?
Ans: A circle can have an infinite number of tangents. A circle is made of infinite points and from each point, a tangent can be formed.
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 ______.
Ans: A tangent to a circle intersects it in exactly one point.
Ans: A line intersecting a circle in two points is called a secant.
Ans: A circle can have two parallel tangents at the most opposite to one another.
Ans: The common point of a tangent to a circle and the circle is called the Point of Contact.
A tangent PQ at a point P of a circle of radius \[\text{5cm}\] meets a line through the centre O at a point Q so that \[\text{OQ = 12cm}\]. Length of PQ is :
Ans: According to the Pythagoras Theorem: \[PQ=\sqrt{\left( O{{Q}^{2}}-\left. O{{P}^{2}} \right) \right.}\]
OQ = \[\text{12}\]cm, OP = \[\text{5}\]cm
Because,
\[PQ=\sqrt{\left( O{{Q}^{2}}-\left. O{{P}^{2}} \right) \right.}\]
\[=\sqrt{\left( {{12}^{2}}-\left. {{5}^{2}} \right) \right.}\]
\[=\sqrt{144-25}\]
\[=\sqrt{119}\]cm.
Hence, (D) is the answer.
Draw a circle and two lines parallel to a given line such that one is tangent and the other, a secant to the circle.
Ans: From the Given Figure below,
Let ‘l’ be the given line and a circle with centre O is drawn.
A tangent to the circle from point B is drawn \[\parallel \] to line ‘l’.
CD is drawn \[\parallel \] to line ‘l’ and is the secant.