Circles Test

Result

Circles Test - 38

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Weekly Quiz Competition

Question 1
1 / -0

In a circle of radius $$13 ~cm, PQ$$ and $$RS$$ are two parallel chords of lengths $$24 ~cm$$ and $$10~ cm$$ respectively. Calculate the distance between the chords if they are $$(i)$$ on the same side of the center and $$(ii)$$ on the opposite sides of the center.

A
$$5~cm,12~cm$$

B
$$7~cm,13~cm$$

C
$$5~cm,17~cm$$

D
$$7~cm,17~cm$$

Solution
Question 2
1 / -0

In Fig. 2 , the measure of $$\angle B C D$$ is:

A
$$100 ^ { \circ }$$

B
$$70 ^ { \circ }$$

C
$$80 ^ { \circ }$$

D
$$30 ^ { \circ }$$
Question 3
1 / -0

In a circle of radius $$2018$$ having center at $$O$$, $$OPQR$$ is a rectangle with $$Q$$ on the circumference of the circle. $$P,R$$ points inside the circle such that $$PQ=504$$. Then $$PR=$$

A
$$2018$$

B
$$504$$

C
$$252$$

D
$$\sqrt {1008} $$

Solution
Question 4
1 / -0

A,B,C and D be the angles of cyclic quadrilateral taken order , then $$cos({ 180 }^{ \circ }+A)$$ + $$cos({ 180 }^{ \circ }+B)$$+$$cos({ 180 }^{ \circ }+C)$$+$$cos({ 180 }^{ \circ }+D)$$is equal to

A
2 (cosA+cosB )

B
2 (cosA+cosD)

C
0

D
4 cos A

Solution
Question 5
1 / -0

A square is inscribed in the circle $${ x }^{ 2 }+{ y }^{ 2 }-6x+8y-103=0$$ with its sides parallel to the coordinate axes . Then the distance of the vertex of this square which is nearest to the origin is :

A
6

B
$$\sqrt { 137 } $$

C
$$\sqrt { 41 } $$

D
13

Solution
Question 6
1 / -0

The value of x and y in tyhe fighure are measure of angles,then x+y is equal to

A
$$
90^{\circ}
$$

B
$$
85^{\circ}
$$

C
$$
75^{\circ}
$$

D
$$
65^{\circ}
$$
Question 7
1 / -0

$$ AB C D$$ is cyclic quadrilateral such that $$AB$$ is a diameter of the circle circumscribing it and $$\angle ADC=130^{ { \circ } },$$ then the value of $$\angle A B C$$ is:

A
$$50 ^ { \circ }$$

B
$$60 ^ { \circ }$$

C
$$120 ^ { \circ }$$

D
$$40 ^ { \circ }$$

Solution
Question 8
1 / -0

What will be the area of the largest square that can be cut out of a circle of radius 10 cm?

A
100 $${ cm }^{ 2 }$$

B
200 $${ cm }^{ 2 }$$

C
300 $${ cm }^{ 2 }$$

D
400 $${ cm }^{ 2 }$$
Question 9
1 / -0

$$\Box ABCD$$ is a cyclic quadrilateral, $$\angle BAD={ 75 }^{ \circ },m\angle ADC={ 85 }^{ \circ }$$. The bisectors of $$\angle ABC$$ and $$\angle BCD$$ meet in the point O. Find m$$\angle BOC.$$

A
$${ 40 }^{ \circ }$$

B
$${ 70 }^{ \circ }$$

C
$${ 80 }^{ \circ }$$

D
$${ 60 }^{ \circ }$$

Solution
Question 10
1 / -0

Consider a circle with center O and radius = 20cm. Find the perpendicular distance of a chord of length 32cm from the center of the circle.

A
20cm

B
18cm

C
14cm

D
12cm

Solution