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class 10th Mathematics Chapter 9 Test 2 | Tangents and Angles of a Circle | Exercise 9.2 & Review Exercise | Punjab Board 2027
class 10th Math Chapter 9 exercise 9.2
Class 10 Mathematics Test 2 based on Tangents and Angles of a Circle is prepared for students following the Punjab Board 2027 Model Papers. This test covers Exercise No. 9.2 and the Review Exercise and includes important objective and subjective questions for Mathematics exam preparation. Students can use this Class 10 Mathematics Unit 9 Test to revise key concepts, practice questions, and improve their preparation for the Punjab Boards 2027 Mathematics examination.
Exercise 9.2 & Review Exercise
T-2
Unit 9: Tangents and Angles of a circle
Time: 5 minutes
(Objective Type)
Total Marks: 5
1. Tick the correct answer.
(1 × 5 = 5)
(i)
Length ℓ of an arc which subtends an angle of
θ radius of a circle of radius
r is calculated by the formula
ℓ =
(ii)
Area A of a sector having angle
θ radius of a circle of radius
r is calculated by the formula
A =
(iii)
If r = 4 and
ℓ = 14 then angle subtends by the arc
in radian measure is θ =
(iv)
If r = 6 and
θ = 60° then length of the arc is
ℓ =
(v)
Angle inscribed in a semi-circle is:
Exercise 9.2 & Review Exercise
T-2
Unit 9: Tangents and Angles of a circle
Time: 35 minutes
(Subjective Type)
Total Marks: 20
2. Write short answers to the following questions:
(6 × 2 = 12)
(i)
A projector casts an image over an arc on a circular wall.
Two observers on the arc segment report one observing a 50° angle.
What is the other angle in the same segment?
(ii)
A cable in a semicircle bridge forms a triangle with the diameter
of the arch. If the cable meets the endpoints of the diameter and
the top of the arch, what is the angle at the top?
(iii)
Prove that area of a sector is
½r²θ, where
θ is in radians.
(iv)
In a circular arch over a monument entrance, two spotlight fixtures
are placed such that they each shine from two different points on
the arch to the same chord PQ on the base of the arch. If the angle
formed at one light is 55°, what is the angle at the second light
on the same side of chord PQ?
(v)
Uzma cut a pizza of radius 14cm into 8 equal slices.
What is the area of one slice (sector)?
(vi)
A circular garden has a walking path forming a quadrilateral
inscribed in it. If one angle is 87°, what is the opposite angle?
Note: Answer the following Questions.
(4 + 4 = 8)
3.
The perimeter and area of a sector are 14cm and 10cm² respectively.
Find the radius of the circle and the central angle of the sector.
4.
A ferris wheel has a radius of 12m. If a passenger travels a distance
of 18m along the circumference of the ferris wheel, what is the angle
(in radians) swept by the passenger’s position from the starting point?
