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CBSE - Class 10 > Mathematics > Circles Worksheets

Free CBSE - Class 10 Mathematics - Circles worksheets

Sample Worksheets

Here is a Sample Worksheet for you to Practice. Download this worksheet to see the answers.

1.

Choose the correct option and give justification. From a point $Q$, the length of the tangent to a circle is $24$ cm and the distance of $Q$ from the centre is $25$ cm. The radius of the circle is

1.

7 cm

 2.

12 cm

 3.

15 cm

 4.

24.5 cm
2.

Choose the correct option and give justification. In Fig. 10.11, if $TP$ and $TQ$ are the two tangents to a circle with centre $O$ so that $\angle POQ = 110^{\circ}$, then $\angle PTQ$ is equal to

1.

$60^{\circ}$

 2.

$70^{\circ}$

 3.

$80^{\circ}$

 4.

$90^{\circ}$
3.

Choose the correct option and give justification. If tangents $PA$ and $PB$ from a point $P$ to a circle with centre $O$ are inclined to each other at angle of $80^{\circ}$, then $\angle POA$ is equal to

1.

$50^{\circ}$

 2.

$60^{\circ}$

 3.

$70^{\circ}$

 4.

$80^{\circ}$
4.
Prove that the tangents drawn at the ends of a diameter of a circle are parallel.
5.
Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.
6.
The length of a tangent from a point $A$ at distance $5$ cm from the centre of the circle is $4$ cm. Find the radius of the circle.
7.
Two concentric circles are of radii $5$ cm and $3$ cm. Find the length of the chord of the larger circle which touches the smaller circle.
8.

A quadrilateral $ABCD$ is drawn to circumscribe a circle (see Fig. 10.12). Prove that $AB + CD = AD + BC$.

9.

In Fig. 10.13, $XY$ and $X'Y'$ are two parallel tangents to a circle with centre $O$ and another tangent $AB$ with point of contact $C$ intersecting $XY$ at $A$ and $X'Y'$ at $B$. Prove that $\angle AOB = 90^{\circ}$.

10.
Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line-segment joining the points of contact at the centre.
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Chapters in CBSE - Class 10 Mathematics

Applications of Trigonometry Worksheet Areas Related to Circles Worksheet Arithmetic Progression Worksheet Constructions Worksheet Coordinate geometry Worksheet Introduction to Trigonometry Worksheet Pair of linear equations in two variable Worksheet Polynomials Worksheet Probability Worksheet Quadratic Equations Worksheet Real numbers Worksheet Statistics Worksheet Surface Areas and Volumes Worksheet Triangles Worksheet

Free Circles Worksheets

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