Circle

Q. Question 14

Circumference of a circle is always

(a) more than three times of its diameter
(b) three times of its diameter
(c) less than three times of its diameter
(d) three times of its radius

Q. If PQ = RS and $\angle ORS={48}^{\circ }$ in the given figure, what are the values of $\angle OPQ$ and $\angle SOR$?

1. ${84}^{\circ }$, ${48}^{\circ }$
2. ${38}^{\circ }$, ${68}^{\circ }$
3. ${48}^{\circ }$, ${84}^{\circ }$
4. ${78}^{\circ }$, ${84}^{\circ }$

Q.

State true or false.
The incircle of an isosceles $\Delta ABC$, with $AB=AC$, touches the sides $AB,BC,CA$ at $D,E$ and $F$ respectively. Then $E$ bisects $BC$.

1. True

2. False

Q. This is a Yin-Yang symbol. What would be the area covered by the Yin (black) region if the radius of the larger circle is, R = 8 cm?

1. 77

Q.

Through any given set of three distinct points A, B, C it is possible to draw at most ___circle(s).

Q. The length of the line from the center of a circle to any point outside the circle will be always _______ it's radius.

1. greater than or equal to
2. less than
3. less than or equal to
4. greater than

Q. From an external point $Q$, the length of tangent to a circle is $12cm$ and the diatance of $Q$ from the centre of circle is $13cm$. The radius of circle (in $cm$ ) is

1. 10
2. 7
3. 5
4. 12

Q. If a wheel covers a distance of 880 m by rotating 1000 times, then circumference of the wheel will be .

1. 0.88 m
2. 22 m
3. 44 m

Q. Match the correct pairs for a circle with a radius of 6 cm.

1. Area
2. Circumference
3. Diameter
4. $36\pi c{m}^2$
5. $12\pi cm$
6. $12cm$

Q. The boundary of a circle is called its circumference.

1. True
2. False

Q. This is a Yin-Yang symbol. What would be the area covered by the Yin (black) region if the radius of the larger circle is, R = 8 cm?

1. 77

Q. If O is the center of the circle, then the value of $\theta$ in the adjoining figure is

1. ${75}^{\circ }$
2. ${90}^{\circ }$
3. ${60}^{\circ }$
4. ${45}^{\circ }$

Q.

If two circles intersect at two distinct points, there are ___ tangents that are common to both the circles.

1. 2

2. 0

3. 1

4. Infinite

Q. 38. AB is a chord of a circle with centre O and radius 4cm. AB is of length 4cm and divides the circle into two segments. Find the area of the minor segment.

Q. Prove that any three points on a circle cannot be collinear.

Q. A line is a circle with infinite radius.

1. False
2. True

Q. A line is a circle with infinite radius.

1. False
2. True

Q. If $r_1=9cm$ and $r_2=5cm$, then find the area of the shaded region. (Use $\pi =\frac{22}{7}$)

1. 176

Q. Question 2
The diameters of front and rear wheels of a tractor are 80 cm and 2m respectively. Find the number of revolutions that rear wheel will make in covering a distance in which the front wheel makes 1400 revolutions.

Q. Find the circumference of the circles with the radius 7cm :(Take $\pi =\frac{22}{7}$)

1. $44cm$
2. $21cm$
3. $28mm$
4. None

Q. 14. A chord of crcle of radius 12 cm subtends an angle of 120degree at the centre .find the area of segment of circle (use pie=3.14 and root 3=1.73)

Q. Question 9
The radius of a circle whose circumference is equal to the sum of the circumferences of the two circles of diameters 36 cm and 20 cm is
(A) 56 cm
(B) 42 cm
(C) 28 cm
(D) 16 cm

Q. If a wheel covers a distance of 880 m by rotating 1000 times, then circumference of the wheel will be .

1. 0.88 m
2. 22 m
3. 44 m

Q.

From the adjoining figure, identify : Major arc

Q. Length of a chord which is at a distance of 12 cm from centre of a circle with radius 13 cm is

1. 8 cm
2. 10 cm
3. 4 cm
4. 5 cm

Q. Find the area of the shaded region in the given figure, where a circular arc of radius 6 cm has been drawn with vertex of an equilateral triangle of side 12 cm as centre and a sector of circle of radius 6 cm with centre B is made.(Take 𝛑=𝟑.𝟏𝟒 and √𝟑= 1.73).

Q.

The Yin-Yang symbol can be explained with the following dimensions. What would be area covered by the Yin (black) region. The radius of the larger circle is, R = 8 cm.

1. 97.75 $c{m}^2$

2. 94.54 $c{m}^2$

3. 98.12 $c{m}^2$

4. 100.57 $c{m}^2$

Q.

Two circles with centres O and O’ of radii 3 cm and 4 cm, respectively, intersect at two points P and Q, such that OP and O’P are tangents to the two circles. Find the length of the common chord PQ.$\left(2marks\right)$

Q. In the given figure , O is the centre of the circle and XOY is a diameter. If XZ is any other chord of the circle, then which of the following is correct?

1. XZ < OZ
2. XY > XZ
3. OX +OZ
4. ZX + ZY

Q. If $z_1$ and $z_2(\pm 0)$ are two complex numbers such that $\left|\frac{z_1-z_2}{z_1+z_2}\right|=1,$ then

1. $z_2=ik{z}_1,k\in R$
2. $z_2=k{z}_1,k\in R$
3. $z_2=z_1$
4. None of these