Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

MATHEMATICS > circles > Flashcards

circles Flashcards

1
Q
  1. A circle has a number of tangents equal to

(a) 0
(b) 1
(c) 2
(d) Infinite

A

(d)Infinite

A circle has infinitely many tangents, touching the circle at infinite points on its circumference.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q
  1. A tangent intersects the circle at:

(a) One point
(b) Two distinct point
(c) At the circle
(d) None of the above

A

(a)One point

A tangent touches the circle only on its boundary and do not cross through it.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q
  1. A circle can have _____parallel tangents at a single time.

(a) One
(b) Two
(c) Three
(d) Four

A

(b)Two

A circle can have two parallel tangents at the most.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q
  1. If the angle between two radii of a circle is 110º, then the angle between the tangents at the ends of the radii is:

(a) 90º
(b) 50º
(c) 70º
(c) 40º

A

(c)70º
If the angle between two radii of a circle is 110º, then the angle between tangents is 180º − 110º = 70º. (By circles and tangents properties)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q
  1. The length of the tangent from an external point A on a circle with centre O is

(a) always greater than OA
(b) equal to OA
(c) always less than OA
(d) Cannot be estimated

A

(c)always less than OA
Since the tangent is perpendicular to the radius of the circle, then the angle between them is 90º. Thus, OA is the hypotenuse for the right triangle OAB, which is right-angled at B. As we know, for any right triangle, the hypotenuse is the longest side. Therefore the length of the tangent from an external point is always less than the OA.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q
  1. AB is a chord of the circle and AOC is its diameter such that angle ACB = 50°. If AT is the tangent to the circle at the point A, then BAT is equal to

(a) 65°
(b) 60°
(c) 50°
(d) 40°

A 
(c)50°
∠ABC = 90 (Angle in Semicircle)
In ∆ACB
∠A + ∠B + ∠C = 180°
∠A = 180° – (90° + 50°)
∠A = 40°
Or ∠OAB = 40°
Therefore, ∠BAT = 90° – 40° = 50°
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q
  1. If TP and TQ are the two tangents to a circle with centre O so that ∠POQ = 110°, then ∠PTQ is equal to

(a) 60°
(b) 70°
(c) 80°
(d) 90°

A

(b)70°

We can see, OP is the radius of the circle to the tangent PT and OQ is the radius to the tangents TQ.
So, OP ⊥ PT and TQ ⊥ OQ
∴ ∠OPT = ∠OQT = 90°
Now, in the quadrilateral POQT, we know that the sum of the interior angles is 360°
So, ∠PTQ + ∠POQ + ∠OPT + ∠OQT = 360°
Now, by putting the respective values, we get,
⇒ ∠PTQ + 90° + 110° + 90° = 360°
⇒ ∠PTQ = 70°

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q
  1. The length of a tangent from a point A at a distance 5 cm from the centre of the circle is 4 cm. The radius of the circle is:
    (a) 3cm
    (b) 5cm
    (c) 7cm
    (d) 10cm
A

(a)3cm

AB is the tangent, drawn on the circle from point A.
So, OB ⊥ AB
Given, OA = 5cm and AB = 4 cm
Now, In △ABO,
OA2 = AB2 + BO2 (Using Pythagoras theorem)
⇒ 52 = 42 + BO2
⇒ BO2 = 25 – 16
⇒ BO2 = 9
⇒ BO = 3
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q
  1. If a parallelogram circumscribes a circle, then it is a:
    (a) Square
    (b) Rectangle
    (c) Rhombus
    (d) None of the above
A

(c)Rhombus

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q
  1. Two concentric circles are of radii 5 cm and 3 cm. The length of the chord of the larger circle which touches the smaller circle is:
    (a) 8
    (b) 10
    (c) 12
    (d) 18
A 
(a)8
From the above figure, AB is tangent to the smaller circle at point P.
∴ OP ⊥ AB
By Pythagoras theorem, in triangle OPA
OA2 = AP2 + OP2
⇒ 52 = AP2 + 32
⇒ AP2 = 25 – 9
⇒ AP = 4
Now, as OP ⊥ AB,
Since the perpendicular from the center of the circle bisects the chord, AP will be equal to PB
So, AB = 2AP = 2 × 4 = 8 cm
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

Two concentric circles of radii a and b (a > b) are given. Find the length of the chord of the larger circle which touches the smaller circle.

a) √a^2+b^2
b) √a^2-b^2
c) 2√a^2-b^2
d) 2√a^2+b^2

A

c)2√a^2-b^2

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q
  1. Three circles touch each other externally. The distance between their centres is 5 cm, 6 cm and 7 cm. Find the radii of the circles.
    a) 2 cm, 3 cm, 4 cm
    b) 1 cm, 2 cm, 4 cm
    c) 1 cm, 2.5 cm, 3.5 cm
    d) 3 cm, 4 cm, 1 cm
A

a)2 cm, 3 cm, 4 cm

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q
  1. A point P is 13 cm from the centre of the circle. The length of the tangent drawn from P to the circle is 12cm. Find the radius of the circle.
    a) 5cm
    b) 7cm
    c) 10cm
    d) 12cm
A

a)5cm

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

In the adjoining figure ‘O’ is the center of circle, ∠CAO = 25° and ∠CBO = 35°. What is the value of ∠AOB?

a) 120°
b) 110°
c) 55°
d) Data insufficient

A

a)120°

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q 
A: What is a line called, if it meets the circle at only one point?
B: Collection of all points equidistant from a fixed point is \_\_\_\_\_\_.
1: Chord
2: Tangent
3: Circle
4: Curve
5: Secant
Which is correct matching?
a)A-2; B-4
b)A-5; B-4
c)A-4; B-1
d)A-2; B-3
A

d)A-2; B-3

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q
  1. A point A is 26 cm away from the centre of a circle and the length of tangent drawn from A to the circle is 24 cm. Find the radius of the circle.
    a) 2√313
    b) 12
    c) 7
    d) 10
A

d)10

17
Q
  1. The quadrilateral formed by joining the angle bisectors of a cyclic quadrilateral is a
    a) cyclic quadrilateral
    b) parallelogram
    c) square
    d) Rectangle
A

a)cyclic quadrilateral

18
Q
  1. ABCD is a cyclic quadrilateral PQ is a tangent at B. If ∠DBQ = 65°, then ∠BCD is
    a) 35°
    b) 85°
    c) 90°
    d) 115°
A

d)115°

19
Q

In a circle of radius 5 cm, AB and AC are the two chords such that AB = AC = 6 cm. Find the length of the chord BC

a) None of these
b) 9.6cm
c) 10.8cm
d) 4.8cm

A

b)9.6cm

20
Q

The distance between the centres of equal circles each of radius 3 cm is 10 cm. The length of a transverse tangent AB is

a) 10cm
b) 8cm
c) 6cm
d) 4cm

A

b)8cm

21
Q

A point P is 10 cm from the center of a circle. The length of the tangent drawn from P to the circle is 8 cm. The radius of the circle is equal to

a) 4cm
b) 5cm
c) None of these
d) 6cm

A

d)6cm

22
Q

In fig, O is the centre of the circle, CA is tangent at A and CB is tangent at B drawn to the circle. If ∠ACB = 75°, then ∠AOB=

a) 75°
b) 85°
c) 95°
d) 105°

A

d)105°

23
Q

In the given figure, PAQ is the tangent. BC is the diameter of the circle. ∠BAQ = 60°, find ∠ABC :

a) 25°
b) 30°
c) 45°
d) 60°

A

b)30°

MATHEMATICS (8 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2024 Bold Learning Solutions. Terms and Conditions