Chapter 10 · Circles

NCERT Class 10 Maths Exercise 10.1

All 4 questions of NCERT Class 10 Maths Exercise 10.1 (Circles), in the book's order, each with its answer and a step-by-step solution.

1. Q1
   How many tangents ​can ​a ​circle ​have?
   Show answer

   A circle has infinitely many tangents, one at each of its infinitely many points.

   Step-by-step solution →
2. Q2
   Fill in ​the blanks:

   1. (i)A tangent to a circle intersects it in ____ point(s).
   2. (ii)A line intersecting ​a circle in two points is ​called ​a ____. ​
   3. (iii)A circle ​can have ​____ parallel tangents at the ​most.
   4. (iv)The common point of a tangent to a circle and the circle is called ____.
   Show answer

   (i) One (ii) secant (iii) two (iv) point of contact.

   Step-by-step solution →
3. 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 :

   1. (a)12 cm
   2. (b)13 cm
   3. (c)8.5 cm
   4. (d)$\sqrt{119}$ cm
   Show answer

   (d) $\sqrt{119}$ cm

   Step-by-step solution →
4. 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.
   Show answer

   Drop the perpendicular from $O$ to $l$ meeting the circle at $P$. The line through $P$ parallel to $l$ is the required tangent ($d=r$), and a line parallel to $l$ through any point $N$ on $OP$ with $ON<r$ is the required secant ($d<r$).

   Step-by-step solution →