CIRCLES-Exercise 10.1
Maths - Exercise
Q1.How many tangents can a circle have?
Answer
A circle can have infinitely many tangents.Reason
Each tangent touches the circle at exactly one point on its circumference. Since a circle has infinitely many points on its circumference, one distinct tangent can be drawn at each such point, giving infinitely many tangents in total.Q2.Fill in the blanks
(i) A tangent to a circle intersects it in one point(s).
(ii) A line intersecting a circle in two points is called a secant.
(iii) A circle can have two parallel tangents at the most.
(iv) The common point of a tangent to a circle and the circle is called point
of contact.
Q3. 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 PQ is :
(A) 12 cm
(B) 13 cm
(C) 8.5 cm
(D) \(\sqrt{119}\) cm
Solution:
By pythagoras theorem, we can find length of \(P\)
\[ \begin{aligned} OP^2&=OP^2+PQ^2\\ 12^2&=5^2+PQ^2\\ PQ^2&=144-25\\ &=119\\ \Rightarrow PQ&=\sqrt{119} \end{aligned} \]Correct Answer is : (D) \(\sqrt{119}\) cm
Q4. 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.
In this Figure, parallel lines
PQ is tangent and
RS is a secant
