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This mock test of Test: Tangents To A Circle for Class 10 helps you for every Class 10 entrance exam.
This contains 25 Multiple Choice Questions for Class 10 Test: Tangents To A Circle (mcq) to study with solutions a complete question bank.
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QUESTION: 1

In the figure, the pair of tangents AP and AQ, drawn from an external point A to a circle with centre O, are perpendicular to each other and length of each tangent is 4 cm, then the radius of the circle is

Solution:

QUESTION: 2

The length of the tangent drawn from a point 8 cm away from the centre of a circle, of radius 6 cm, is :

Solution:

Since tangent is perpendicular to radius, the triangle so formed is a right angled triangle,

So using Pythagoras Theorem,

Line joining centre and And the point outside the circle is hypotenuse and tangent and radius are the two sides

H^{2}=P^{2}+B^{2}

64=P^{2}+36

P=

QUESTION: 3

Number of tangents, that can be drawn to a circle, parallel to a given chord is

Solution:

There are only two tangents that can be drawn parallel to a given chord. That is the tangents are drawn on either side of the chord so that both are parallel to the chord.

QUESTION: 4

How many tangents can be drawn to a circle from a point in its interior?

Solution:

QUESTION: 5

The tangents drawn at the ends of a diameter of a circle are:

Solution:

QUESTION: 6

A circle can pass through

Solution:

The answer can be 2 collinear points as well. We have three collinear points. Join one point to the other two points and then draw the perpendicular bisector for both the lines

Join the perpendicular bisectors. The point is the centre of the circle. And a circle can be formed then. Also two points can form a circle as the two points joines becomes a diameter.

Option D : The number of circles which can pass through three given non-collinear points is exactly one.

So, A is the correct Option

QUESTION: 7

In the given figure, PA and PB are tangents from P to a circle with centre O. If ∠AOB = 130°, then find ∠APB.

Solution:

In AOB, by angle sum property

Angle A + Angle B + Angle O=180°

2Angle A = 50° (Triangle is isosceles triangle)

Angle A = 25°

We know Angle APB= 2Angle A

Angle APB=2*25= 50°

QUESTION: 8

From a point A, the length of a tangent to a circle is 8cm and distance of A from the circle is 10cm. The length of the diameter of the circle is

Solution:

QUESTION: 9

PQ is a tangent drawn from a point P to a circle with centre O and QOR is a diameter of the circle such that ∠POR =120^{o}, then find ∠OPQ.

Solution:

QUESTION: 10

If figure 1, O is the centre of a circle, PQ is a chord and PT is the tangent at P. If ∠POQ = 70^{o}, then ∠TPQ is equal to

Solution:

POQ is an isosceles triangle because of 2 radii as sides. So by angle sum property, 2*angle OPQ=180-70=110

Angle OPQ=55°

Since Angle TPO is a right angle , because PT is a tangent,

Angle OPQ+Angle TPQ=90

Angle TPQ=90° - 55° = 35°

QUESTION: 11

A line that intersects a circle in exactly one point is called a

Solution:

QUESTION: 12

A line that intersects a circle in two distinct points is called a

Solution:

A chord is the actual line segment determined by these two points, that is, the interval on the secant whose ends are at these positions But a secant of a curve is a line that intersects the curve at a minimum of two distinct points. The difference is that the secant is not just limited to the circle it extends further.

QUESTION: 13

The length of tangent drawn from an external point P to a circle, with centre O, is 8 cm. If the radius of the circle is 6 cm, then the length of OP (in cm) is:

Solution:

QUESTION: 14

A line segment having its end points on the circle is called a

Solution:

QUESTION: 15

Number of tangents from a point lying inside the circle is

Solution:

QUESTION: 16

The angle between two tangents drawn from an external point to a circle is 110°. The angle subtended at the centre by the segments joining the points of contact to the centre of circle is:

Solution:

QUESTION: 17

A tangent PA is drawn from an external point P to a circle of radius 3√2 cm such that the distance of the point P from O is 6 cm as shown figure. The value of ∠APO is

Solution:

**The correct answer is c**

**In right angled triangle, OAP**

**sin of angle APO = AO/OP = 1/root2**

**sin 45 = 1/root2**

**angle APO = 45 degree**

QUESTION: 18

What is the distance between two parallel tangents of a circle of the radius 4 cm?

Solution:

QUESTION: 19

In fig., two concentric circles of radii a and b (a > b) are given. The chord AB of larger circle touches the smaller circle at C. The length of AB is:

Solution:

QUESTION: 20

A tangent to a circle is a line that intersects the circle in

Solution:

QUESTION: 21

In the figure, if from an external point T, TP and TQ are two tangents to a circle with centre O so that POQ = 110°, then, PTQ is:

Solution:

QUESTION: 22

In fig., two circles with centres A and B touch each other externally at k. The length of PQ (in cm) is

Solution:

QUESTION: 23

The distance between two parallel tangents to a circle of radius 5 cm is

Solution:

QUESTION: 24

A circle may have…….

Solution:

QUESTION: 25

In fig., PA is a tangent to a circle of radius 6 cm and PA = 8 cm, then length of PB is

Solution:

### Number of Tangents from a Point to a Circle

Video | 05:33 min

### Construction of two tangents from an external point to a circle

Video | 03:29 min

### Angles formed by the Tangents & Secants of a Circle

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