Circles Test

Result

Circles Test - 9

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Weekly Quiz Competition

Question 1
1 / -0

The radius of a circle is 25 cm. AB and CD are two parallel chords 17 cm apart. If AB = 48 cm, then CD is approximately equal to

A
48 cm

B
24 cm

C
46 cm

D
42 cm

Solution

AE = 24 cm
AO = 25 cm

So, EO = Therefore, FO = 17 - 7 cm = 10 cm

Now, FO = 10 cm
CO = 25 cm
CF =
CD = 2 × 22.9 = 45.8 cm or 46 cm approx.
Question 2
1 / -0

In the given figure, two chords AB and CD of a circle intersect each other at a point E such that BAC = 45⁰, BED = 120⁰. Find ABD.

A
5⁰

B
30⁰

C
45⁰

D
60⁰
Question 3
1 / -0

In given figure, a circle and a quadrilateral ABCD inscribed in it is shown. If B = 135⁰, E is equal to

A
45⁰

B
125⁰

C
130⁰

D
62.5⁰
Question 4
1 / -0

In the adjoining figure, ABC is a right angled triangle with AB = 6 cm and AC = 8 cm. The radius of the inner circle is

A
2 cm

B
1 cm

C
6 cm

D
8 cm

Solution
Question 5
1 / -0

AB and CD are parallel chords with centre O such that AB = 80 cm and CD = 18 cm. The chords are on the same side of the centre and the distance between them is 31 cm. The radius of the circle is

A
17 cm

B
43 cm

C
21 cm

D
41 cm
Question 6
1 / -0

In the given figure, AOB and COD are two diameters of a circle with centre O. If OAC= 70°, find ABD.

A
40°

B
70°

C
50°

D
80°
Question 7
1 / -0

In the given figure, chord AB is shown in a circle. If two more chords AD and BE are drawn perpendicular to AB, which of the following holds true?

A
AD = BE

B
AD = 2BE

C
2AD = BE

D
none of these
Question 8
1 / -0

In the figure shown below, PT and PB are tangent and secant to the circle respectively, PT = 6 cm and PA = 6 cm. Find AB.

A
0 cm

B
9 cm

C
4 cm

D
16 cm
Question 9
1 / -0

What is the distance (in cm) between two parallel chords of lengths 48 cm and 14 cm in a circle of radius 25 cm?

A
7 cm

B
14 cm

C
21 cm

D
31 cm

Solution

r = 25 cm
r₁ = 48/2 = 24 cm
r₂ = 14/2 = 7 cm
d =
=
= 30.96 = 31 cm
Question 10
1 / -0

In the given figure, ABCD is a quadrilateral inscribed in a circle. Diagonals AC and BD are joined. If CAD = 40° and BDC = 25°, find the measure of BCD.

A
85°

B
120°

C
115°

D
95°
Question 11
1 / -0

PQ and PR are tangents to a circle and QS is the diameter. Then

A
QPR = RQS

B
QPR = 2RQS

C
QPR = RQS

D
none of the foregoing
Question 12
1 / -0

In the given figure, A is a point outside the circle with centre O. AT and AU are tangents to the circle and P is the point on the circle as shown in the figure below. Find TPU (given that TAU = 80^o).

A
130^o

B
110^o

C
250^o

D
150^o
Question 13
1 / -0

The figure shows a circle of diameter AB and radius 12.5 cm. If chord CA is 24 cm, find the area of triangle ABC.

A
60 cm²

B
84 cm²

C
40 cm²

D
52 cm²

Solution

r = DB = 12.5 cm = AB = 2 x 12.5 = 25 cm
CA = 24 cm
ACC to Pythagoras theorem
CB =
=
=
CB = = 34.6 = 25 cm
Area & = Base side
24 + 25 + 35 = 84 cm²
Question 14
1 / -0

Two chords AB and CD of a circle cut each other when produced outside the circle at P. AD and BC are joined.

If PAD = 30° and CPA = 45°, find CBP.

A
95°

B
105°

C
135°

D
None of these

Solution

DAB = BCD = 30°(Angle subtended by the same arc at any point except centre is equal)
In ΔBCP, CBP = 180°- BCP - CBP
= 180° - 30°- 45° = 105°
Question 15
1 / -0

ABCD is a quadrilateral. If ACB = ADB, then

A
ABCD is a cyclic quadrilateral

B
ABCD is a parallelogram

C
ABCD is a square

D
ABCD is a cyclic rectangle.

Solution

As ACB = ADB (Angles in the same segment)
So, we can say ABCD is a cyclic quadrilateral.
Question 16
1 / -0

In the figure below, find ADB if BAQ = 58⁰.

A
144⁰

B
122⁰

C
48⁰

D
96⁰
Question 17
1 / -0

A chord of a circle is equal to the radius. The angle subtended by the chord at the minor arc of the circle is

A
150⁰

B
60⁰

C
90⁰

D
30⁰

Solution

As shown in the diagram
The CBA would is 150^o .
Question 18
1 / -0

In the given figure, ABC is inscribed in a circle. The bisector of BAC meets BC at D and the circle at E. If EC is joined, then ECD = 40°.

Find the measure of BAC.

A
30°

B
40°

C
50°

D
80°

Solution

BAE = BCE = 40°(Angles in the same segment are equal)
BAC = 2 BAE = 80° (AD is the bisector of BAC)
Question 19
1 / -0

As shown in figure, ABC is a triangle inscribed in a circle with centre O. A is equal to

A
30^o

B
60^o

C
45^o

D
75^o
Question 20
1 / -0

In the following figure AP, AQ and BC are tangents to a circle. The length of AP = 12 cm. Find the perimeter of the triangle ABC.

A
36 cm

B
22 cm

C
24 cm

D
40 cm

Solution