Circles

Q.

All three circles are tangents to the same line and also to each other. Circles C2 and C3 have equal radii. Find the radius of C2, if the radius of C1 is equal to 10 cm.

1. 30 cm

2. 35 cm

3. 40 cm

4. 45 cm

Q.

Two circles of radii 8 cm and 3 cm have their centers 13 cm apart. Find the length of a direct common tangent to the two circles.

__

Q. Prove that the tangents drawn at the ends of diameter of a circle are parallel

Q.

In the given figure, PT is tangent to the circle at T. If PA = 4 cm and AB = 5 cm, find PT. AB is equal to diameter.

Q.

C is a point on the minor arc AB of the circle with centre O. Given ∠ACB = x. Calculate ∠x , if ACBO is a parallelogram.



1. $x={10}^{\circ }$

2. $x={90}^{\circ }$

3. $x={120}^{\circ }$

4. $x={87}^{\circ }$

Q. Two circles having radii 3.5 cm and 4.8 cm touch each other internally. Find the distance between their centres.

Q. The external and internal radii of a hollow hemispherical vessel are $15\text{cm}$ and $10\text{cm}$ respectively. The approximate cost of painting it at the rate of $₹2$ per $\text{sq. cm}$ is:

1. $₹4,850$
2. $₹4,860$
3. $₹4,870$
4. $₹4,880$

Q.

In the given figure, O is the centre of the circle & $\angle ACB={60}^{\circ }$, Find angle OAB.

1. ${70}^{\circ }$

2. ${120}^{\circ }$

3. ${30}^{\circ }$

4. ${110}^{\circ }$

Q.

7. Fill in the blanks :

(v) Total number of diameters of a circle is ______ .

Q. Question 6 (ii)
The volume of a right circular cone is $9856c{m}^3$. If the diameter of the base is 28 cm, find slant height of the cone.
$[Assume\pi =\frac{22}{7}]$

Q.

In the given figure, PQ is a diameter and chord SR is parallel to PQ. Given that $\angle PQR={58}^{\circ },$ calculate $\angle RPQ.$

1. $\angle RPQ={32}^{\circ }$

2. $\angle RPQ={62}^{\circ }$

3. $\angle RPQ={39}^{\circ }$

4. $\angle RPQ={82}^{\circ }$

Q.

In the following figure, AD is a straight line. OP $\perp$ AD and O is the centre of both the circles. If OA = 34 cm, OB = 20 cm and OP = 16 cm; find the length of AB.

1. 20 cm

2. 18 cm

3. 30 cm

4. 10 cm

Q. Chord of a circle is always bisected by the radius of that circle.

1. False
2. True

Q.

Find the length of circumradius of a right-angled triangle whose adjacent sides are 3cm and 4cm?

1. 2 cm

2. 2.5 cm

3. 3 cm

4. 3.5 cm

Q.

In the given, PQ is a diameter. Chord SR is parallel to PQ. Given that $\angle PQR={58}^{\circ }$ Calculate: $\angle STP$

1. ${208}^{\circ }$

2. ${18}^{\circ }$

3. ${148}^{\circ }$

4. ${104}^{\circ }$

Q.

The longest chord of a circle is .

Q.

Find the distance of point P from the centre of circle given the radius is 5 cm & length of tangent PA is 12 cm

1. 9

2. 18

3. 7

4. 13

Q.

___ is a line that intersects a circle at only one point, and ___ is a line that intersects the circle at two distinct points.

1. Secant, tangent

2. Tangent, tangent

3. Secant, secant

4. Tangent, secant

Q.

Any two points A and B on the circle are always at a fixed distance from a fixed point O. The point O is ___.

1. circumference

2. arc

3. radius

4. center

Q.

Fill in the blanks:

If we join any $2$ points of a circle we get ____________

Q. Identify the major arc, the minor arc, and the centre in the following figure.

1. Minor arc
2. Centre
3. Major arc

Q. A circle has radius 15 cm. Find the length of its longest chord?

Q. State whether True or False:
A line can be taken as a circle with infinite radius and a circle can be assumed to be a polygon with infinite sides.

1. False
2. True

Q.

A circular garden of radius $10m$ has a straight line fence between the two points on the boundary of the garden. The fence lies inside the garden arena. This fence separates the walking area which is a small region from the plants. The fence is at a distance of $6m$ from the centre of the garden. What is the walking area in $m^2$? It is given that $\cos {53}^{\circ }=\frac{3}{5}$.

1. 36

2. 44.5

3. 12

4. 72

Q. The radii of the internal and external surfaces of a metallic spherical shell are $3\text{cm}$ and $5\text{cm}$ respectively. It is melted and recast into a solid right circular cylinder of height $10.67\text{cm}$. Then, the diameter of the base of the cylinder is approximately:

1. $6\text{cm}$
2. $7\text{cm}$
3. $8\text{cm}$
4. $5\text{cm}$

Q.

There is a tent in a conical shape. The slant height of the tent is 14 m. If the curved surface area of the tent is 308 m² , then what is the base area of the tent? (Take $\pi =\frac{22}{7}$)

Q. In the given figure, O is the centre of the circle and B is a point of contact. seg OE ⊥ seg AD, AB = 12, AC = 8, find
(1) AD (2) DC (3) DE.

Q.

ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If $\angle DBC={70}^{\circ }$ and $\angle BAC={30}^{\circ }$, then find $\angle BCD$. Further, if AB = BC, then find $\angle ECD$.

[3 Marks]

Q. The radius and height of a right circular cone are in the ratio $3:4$. If its slant height is $25\text{cm}$, its total surface area is:

1. $375\pi {\text{cm}}^2$
2. $225\pi {\text{cm}}^2$
3. $600\pi {\text{cm}}^2$
4. $500\pi {\text{cm}}^2$

Q. A circle is a polygon with infinite number of sides.

1. True
2. False