Description

This mock test of Test: Properties Of Tangents for Class 10 helps you for every Class 10 entrance exam.
This contains 15 Multiple Choice Questions for Class 10 Test: Properties Of Tangents (mcq) to study with solutions a complete question bank.
The solved questions answers in this Test: Properties Of Tangents quiz give you a good mix of easy questions and tough questions. Class 10
students definitely take this Test: Properties Of Tangents exercise for a better result in the exam. You can find other Test: Properties Of Tangents extra questions,
long questions & short questions for Class 10 on EduRev as well by searching above.

QUESTION: 1

PT is a tangent from an external point P and PAB is a secant. If PT = 6cm and PA = 3cm, then the length of PB is __

Solution:

We know that:

PT^{2} = PA X PB

therfore PB = PT^{2}/PA = 36/3 = 12

QUESTION: 2

A circle is inscribed in a ΔABC having AB = 10cm, BC = 12cm and CA = 8cm and touching these sides at D, E, F respectively. The lengths of AD, BE and CF will be

Solution:

QUESTION: 3

In the given figure, AR = 5cm, BR = 4cm and AC = 11cm. What is the length of BC?

Solution:

Since the sides of the triangles are tangent to the circle. BR = BP,AR = AQ and CP = CQ

So, BP = 4cm and AQ = 5

CQ = 11-5 = 6 = CP

BC = BP + CP = 4 + 6 = 10 cm

QUESTION: 4

In given figure, the length of BC is

Solution:

QUESTION: 5

Segment joining the points of contact of two parallel tangents

Solution:

QUESTION: 6

In a circle with centre O, AB and CD are two diameters perpendicular to each other. The length of chord AC is

Solution:

QUESTION: 7

If in the given figure radius of smaller and larger circles be 4 and 5 cm. Find the length of chord AB.

Solution:

QUESTION: 8

A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is :

Solution:

QUESTION: 9

The maximum number of common tangents that can be drawn to two circles intersecting at two distinct point is

Solution:

QUESTION: 10

In a circle of radius 7cm, tangent PT is drawn from point P such that PT = 24cm. If O is the centre of the circle, then the length of OP is:

Solution:

QUESTION: 11

In the figure, PQ is a tangent at a point R of the circle with centre O. If ∠TRQ = 30°.The measure of ∠PRS is

Solution:

QUESTION: 12

In the given figure, length of BC is:

Solution:

QUESTION: 13

ABC is a right triangle right angled at B such that BC = 6 cm and AB = 8 cm. The radius of its incircle is

Solution:

By pythagoras theorem ,

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

=36 + 64=100

H=10

We have a square BPOQ so all sides are equal.

Since tangents from a point are equal in length

Let AP = AR = x

BP=BQ=y

RC = QC = z

x + y = 8

x = 8 - y

x + z = 10 ⇒ 8 - y + z = 10 ⇒ z = 2 + y

y + z = 6 ⇒ y + 2 + y = 6 ⇒ y = 2

x = 6, z= 4

Since BP = OQ = y = 2

QUESTION: 14

Quadrilateral ABCD circumscribes a circle as shown in figure. The side of the quadrilateral which is equal to AP + BR is:

Solution:

QUESTION: 15

If the angle between two radii of a circle is 100°, then angle between the tangents at the ends of those radii is:

Solution:

### Tangents at the Origin

Doc | 12 Pages

### Geonet properties and test methods

Doc | 8 Pages

### Theorem on Lengths of Tangents

Video | 10:07 min

### Examples : Tangents and Normals

Video | 13:50 min

- Test: Properties Of Tangents
Test | 15 questions | 15 min

- Test: Construction Of Tangents
Test | 10 questions | 10 min

- Test: Tangents To A Circle
Test | 25 questions | 25 min

- Test: Tangents And Normals
Test | 10 questions | 10 min

- Test: DFT Properties
Test | 10 questions | 10 min