PYQ Vault

Area of the minor or major segment cut off by a chord subtending a central angle

This type of question, asked 5 times: CDS 2 2020, CDS 2 2021, CDS 2 2022, CDS 1 2024, CDS 2 2026. All 5 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 2 2020

    86
    What is the area of a segment of a circle of radius r subtending an angle θ\theta at the centre ?

    Tap an option to check your answer.

  2. Question 2 (case study, 2 parts)

    CDS 2 2021

    Consider the following for the next two (02) items that follow : A chord of a circle of radius 2.1 cm subtends an angle of 120∘120^\circ at the centre. (take π=227\pi = \frac{22}{7} and 3=1.732\sqrt{3} = 1.732)
    79
    What is the approximate area of minor segment of the circle ?

    Tap an option to check your answer.

    80
    What is the approximate area of major segment of the circle ?

    Tap an option to check your answer.

  3. Question 3 (case study, 2 parts)

    CDS 2 2022

    Consider the following for the next two (02) items that follow : A chord of length ll of a circle makes an angle 90∘90^\circ at the centre of the circle.
    74
    What is the area of the minor segment ?

    Tap an option to check your answer.

    75
    What is the area of the major segment ?

    Tap an option to check your answer.

  4. Question 4

    CDS 1 2024

    39
    The chord AB of a circle with centre at O is 232\sqrt{3} times the height of the minor segment. If P is the area of the sector OAB and Q is the area of the minor segment of the circle, then what is the approximate value of PQ\frac{P}{Q} ? (Take 3=1.7\sqrt{3} = 1.7 and π=3.14\pi = 3.14)

    Tap an option to check your answer.

  5. Question 5

    CDS 2 2026

    53
    A chord of a circle makes an angle of 90∘90^\circ at the centre of the circle. If the area of the major segment is k times the area of the minor segment, then what is the value of k ? (Take π=227\pi = \frac{22}{7})

    Tap an option to check your answer.