Test: Tangents to a Circle - Class 10 MCQ

# Test: Tangents to a Circle - Class 10 MCQ

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## 25 Questions MCQ Test Mathematics (Maths) Class 10 - Test: Tangents to a Circle

Test: Tangents to a Circle for Class 10 2024 is part of Mathematics (Maths) Class 10 preparation. The Test: Tangents to a Circle questions and answers have been prepared according to the Class 10 exam syllabus.The Test: Tangents to a Circle MCQs are made for Class 10 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Tangents to a Circle below.
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Test: Tangents to a Circle - 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

Detailed Solution for Test: Tangents to a Circle - Question 1

Join OA.

Triangles OPA and OQA are congruent.

⇒∠PAO = ∠QAO = 45o

Tangent and radius are perpendicular at the point of contact.

∠OPA = 90o

⇒∠OAP = ∠AOP = 45o

⇒OP = AP = 4cm

So the radius of the circle is 4 cm.

Test: Tangents to a Circle - 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 :​

Detailed Solution for Test: Tangents to a Circle - Question 2

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
H2=P2+B2
64=P2+36
P=

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Test: Tangents to a Circle - Question 3

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

Detailed Solution for Test: Tangents to a Circle - Question 3

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.

Test: Tangents to a Circle - Question 4

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

Test: Tangents to a Circle - Question 5

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

Test: Tangents to a Circle - Question 6

A circle can pass through​

Detailed Solution for Test: Tangents to a Circle - Question 6

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

Test: Tangents to a Circle - 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.

Detailed Solution for Test: Tangents to a Circle - Question 7

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°

Test: Tangents to a Circle - 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

Test: Tangents to a Circle - 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 =120o, then find ∠OPQ.

Test: Tangents to a Circle - 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 = 70o, then ∠TPQ is equal to

Detailed Solution for Test: Tangents to a Circle - Question 10

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°

Test: Tangents to a Circle - Question 11

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

Test: Tangents to a Circle - Question 12

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

Detailed Solution for Test: Tangents to a Circle - Question 12

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.

Test: Tangents to a Circle - 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:​

Test: Tangents to a Circle - Question 14

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

Test: Tangents to a Circle - Question 15

Number of tangents from a point lying inside the circle is​

Test: Tangents to a Circle - 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:

Test: Tangents to a Circle - 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

Detailed Solution for Test: Tangents to a Circle - Question 17

In right angled triangle,  OAP

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

sin 45 = 1/root2

angle APO = 45 degree

Test: Tangents to a Circle - Question 18

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

Test: Tangents to a Circle - 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:

Detailed Solution for Test: Tangents to a Circle - Question 19

In ΔAOC
OA2 = AC2 + OC2
a2 = AC2 + b2
a2- b2 = AC2
√a2 - b2 = AC
AB = 2AC
AB = 2√a2 - b2

Test: Tangents to a Circle - Question 20

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

Test: Tangents to a Circle - 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:

Test: Tangents to a Circle - Question 22

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

Test: Tangents to a Circle - Question 23

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

Test: Tangents to a Circle - Question 24

A circle may have…….​

Test: Tangents to a Circle - Question 25

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

## Mathematics (Maths) Class 10

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## Mathematics (Maths) Class 10

116 videos|420 docs|77 tests