Circles Test

Result

Circles Test - 8

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Weekly Quiz Competition

Question 1
1 / -0

RS is the diameter of the circle as shown in the diagram. P is a point lying outside the circle. RPS is

A
90⁰

B
greater than 90⁰

C
less than 90⁰

D
cannot be determined

Solution

As seen from triangle SUP,
∠U = 90°
So, ∠SPR will be less than 90°.
Question 2
1 / -0

In the given figure, O is the centre of the circle. If DAC = 54^o and ACB = 63^o, then BAC =

A
72^o

B
54^o

C
27^o

D
90^o

Solution
Question 3
1 / -0

In the figure given below, O is the centre of the circle. Line AB is tangent to the circle and B is the point of contact, and line DC is also the tangent to the circle and C is the point of contact. If the circle has a radius of 3 cm, then AC is equal to

A
4 cm

B
(2 + ^₎ cm

C
(4 + ^₎ cm

D
3(1 + ) cm

Solution

OC = OB = 3 cm
In right ΔABO, OC = AB = OB = 3 cm
OA² = OB² + AB²
OA² = 9 + 9 = 18
OA² = 3
AC = OA + OC = 3 + 3 = 3 (1 + ) cm
Option 4 is correct.
Question 4
1 / -0

In the given figure, AB is the diameter of the circle.

If PAB = 45° and AQB = 25°, then BPR is equal to

A
50°

B
35°

C
20°

D
25°

Solution

PAB = PBA = 45°
QAB + AQB + ABQ = 180°45° + 25° + ABQ = 180°
ABQ = 110°
PBQ + PQB = 90°
PBQ = 90° - 25° = 65°
PBR = PBA + ABR
= 65° + 180° - ABQ
= 65° + 180° - 110°
= 65° + 70°
= 135°
PBR = 135°
PRB = PQB = 25°
PBR + PRB + BPR = 180°
135° + 25° + BPR = 180°
BPR = 20°
Option 3 is correct.
Question 5
1 / -0

Given a circle as shown in the figure below. If the length of arc ABC is 12 cm, then length of arc ADC is

A
12 cm

B
8 cm

C
16 cm

D
Cannot be determined from the given data

Solution

As the circumferential distance between A and C is unknown the answer cannot be determined by the given data.
Question 6
1 / -0

In the given figure, AOB is a diameter of a circle with centre O. If BOD = 140°, then find the measure of ACD.

A
20°

B
40°

C
60°

D
90°

Solution

BOD = 140°(Given)
BOD + DOA = 180° (Sum of angles on a straight line)
DOA = 40°
DOA = 2ACD (Angle made by the chord at the centre is twice that subtended by it at the circumference)
40° = 2ACD
ACD = 20°
Option (1) is correct.
Question 7
1 / -0

A triangle ABC is inscribed in a circle and the bisectors of the angles meet the circumference at X, Y, Z. The angles of the triangle XYZ are

A
90^o – , 90^o – , 90^o –

B
90^o, 60^o, 30^o

C

D

Solution

If AX, BY and CZ is bisector of angle A, B and C respectively,
X = (B/2) + (C/2)
Y = (A/2) + (C/2)
Z = (A/2) + (B/2)
Question 8
1 / -0

In the given figure, O is the centre of the circle. If ACB = OAB, then the measure of AOB is

A
36^o

B
90^o

C
70^o

D
135^o

Solution

OAB is an isosceles triangle because OA and OB are the radii of the circle.

Let OAB = x = OBA

So, ACB = x

AOB = 2 ACB (angle formed by a chord at the centre is twice the angle formed by it at any point on the same segment of the circle)

AOB = 2x

2x + x + x = 180^ox = 45^oHence, AOB = 90^o
Question 9
1 / -0

The chord of the larger of two concentric circles is tangent to the smaller circle and has length `k`. The area enclosed between the concentric circles is

A
k²

B

C

D
cannot be determined from given data
Question 10
1 / -0

In the following figure, O is the centre of the circle. Find the value of x.

A
30⁰

B
45⁰

C
60⁰

D
75⁰

Solution

Angle subtended by diameter/semicircle on any point of circle is 90°.
Hence, Angle ABD = 90° - 60° = 30°

So, here ∠x = 180° - 60° - 75° = 45°
Question 11
1 / -0

A regular decagon (with 10 sides) is inscribed in a circle. The angle that each side of the decagon subtends at the centre is

A
100⁰

B
42⁰

C
36⁰

D
24⁰
Question 12
1 / -0

If the diameter of the inner circle is half that of the outer circle, find the area of the shaded portion.

A
49 cm²

B
147/4 cm²

C
147/16 cm²

D
49/16
Question 13
1 / -0

A telegraph wire spans 20 m with a dip at the centre of 5 cm. Assuming the wire is in the form of a circular arc, its radius is

A
45 m

B
116 m

C
208 m

D
none of these
Question 14
1 / -0

In the given figure, ABCD is a quadrilateral inscribed in a circle. Diagonals AC and BD are joined. If BAD = 50⁰ and BDC = 45⁰. Find BCD.

A
75⁰

B
105⁰

C
130⁰

D
60⁰
Question 15
1 / -0

The length of a chord of a circle is equal to the radius of the circle. The angle which this chord subtends on the longer segment of the circle is equal to

A
30⁰

B
45⁰

C
60⁰

D
90⁰
Question 16
1 / -0

The length l of a tangent, drawn from a point A to the circle is of the radius r. The distance from A to the centre of circle is

A
r

B
r

C
l

D
l
Question 17
1 / -0

Two concentric circles are of radii 20 cm and 13 cm respectively. A line PQRS cuts one circle at P and S and the other at Q and R. If QR = 10 cm, then PS is equal to

A
32 cm

B
22 cm

C
25 cm

D
12.5 cm
Question 18
1 / -0

A circle with radius 4 units is intersected by a line at points R and T. The maximum possible distance between R and T is

A
1 unit

B
2units

C
4units

D
8 units
Question 19
1 / -0

In the given circle ABCD, O is the centre and ACB is equal to

A
42°

B
45°

C
55°

D
60°
Question 20
1 / -0

Maximum number of common tangents that could be drawn to two given circles is __

A
1

B
2

C
3

D
4

Solution

Maximum number of common tangents that could be drawn to two given circles is
4 if circles are far apart.
3 if they are touching externally.
2 if they intersect each other.
1 if they are touching internally.
0 if one is inside the other and don't touch each other.