Chapter 9 · Circles

NCERT Exemplar Class 10 Maths Exercise 9.1

All 10 questions of NCERT Exemplar Class 10 Maths Exercise 9.1 (Circles), in the book's order, each with its answer and a step-by-step solution.

1. Q1
   If ​radii of ​two ​concentric circles are ​4 ​cm ​and 5 ​cm, then the length of each chord of ​one circle which is tangent to the other circle is

   1. (a)$3$ cm
   2. (b)$6$ cm
   3. (c)$9$ cm
   4. (d)$1$ cm
   Show answer

   (b) $6$ cm

   Step-by-step solution →
2. Q2
   In ​Fig. 9.3, ​if $\angle AOB=125^{\circ }$, then $\angle COD$ ​is ​equal to

   1. (a)$62.5^{\circ }$
   2. (b)$45^{\circ }$
   3. (c)$35^{\circ }$
   4. (d)$55^{\circ }$
   Show answer

   (d) $55^{\circ }$

   Step-by-step solution →
3. Q3
   In Fig. 9.4, $AB$ is ​a ​chord of the circle ​and $AOC$ is its diameter such that $\angle ACB=50^{\circ }$. If $AT$ is the tangent to the ​circle ​at ​the point $A$, ​then $\angle BAT$ ​is equal to

   1. (a)$65^{\circ }$
   2. (b)$60^{\circ }$
   3. (c)$50^{\circ }$
   4. (d)$40^{\circ }$
   Show answer

   (c) $50^{\circ }$

   Step-by-step solution →
4. Q4
   From a ​point P which is at a ​distance of 13 cm from the centre O of a ​circle of ​radius 5 cm, the pair ​of ​tangents PQ and PR to the circle are drawn. Then the area ​of the quadrilateral ​PQOR is

   1. (a)$60$ cm${}^2$
   2. (b)$65$ cm${}^2$
   3. (c)$30$ cm${}^2$
   4. (d)$32.5$ cm${}^2$
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   (a) $60$ cm${}^2$

   Step-by-step solution →
5. Q5
   At ​one ​end A of a diameter AB of a circle of radius 5 cm, tangent XAY is ​drawn to the circle. ​The length of the chord CD parallel ​to XY and at a distance 8 cm from A is

   1. (a)4 cm
   2. (b)5 cm
   3. (c)6 cm
   4. (d)8 cm
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   (d) 8 cm

   Step-by-step solution →
6. Q6
   In ​Fig. ​9.5, $AT$ ​is a tangent ​to the circle with ​centre $O$ such that $OT=4\text{cm}$ and $\angle OTA=30^{\circ }$. Then $AT$ ​is equal to

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

   (c) $2\sqrt{3}$ cm

   Step-by-step solution →
7. Q7
   In Fig. 9.6, if O is the ​centre of a circle, ​PQ ​is a ​chord and the tangent ​PR ​at P ​makes an angle ​of 50 degrees with PQ, then $\angle POQ$ is equal to

   1. (a)$100^{\circ }$
   2. (b)$80^{\circ }$
   3. (c)$90^{\circ }$
   4. (d)$75^{\circ }$
   Show answer

   (a) $100^{\circ }$

   Step-by-step solution →
8. Q8
   In ​Fig. 9.7, if PA ​and PB are tangents ​to ​the ​circle with centre O such that $\angle APB=50^{\circ }$, ​then $\angle OAB$ is equal ​to

   1. (a)$25^{\circ }$
   2. (b)$30^{\circ }$
   3. (c)$40^{\circ }$
   4. (d)$50^{\circ }$
   Show answer

   (a) $25^{\circ }$

   Step-by-step solution →
9. Q9
   If ​two tangents inclined ​at an angle $60^{\circ }$ are ​drawn to ​a circle of radius 3 cm, then ​length of ​each tangent ​is equal ​to

   1. (a)$\frac{3}{2}\sqrt{3}$ cm
   2. (b)$6$ cm
   3. (c)$3$ cm
   4. (d)$3\sqrt{3}$ cm
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   (d) $3\sqrt{3}$ cm

   Step-by-step solution →
10. Q10
    In ​Fig. 9.8, if $PQR$ is the tangent to a ​circle at $Q$ whose centre is $O$, $AB$ ​is ​a chord ​parallel to $PR$ ​and $\angle BQR=70^{\circ }$, ​then $\angle AQB$ is equal to

    1. (a)$20^{\circ }$
    2. (b)$40^{\circ }$
    3. (c)$35^{\circ }$
    4. (d)$45^{\circ }$
    Show answer

    (b) $40^{\circ }$

    Step-by-step solution →