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Circles

SSC CGL Quant. Try each one first, then open its answer.

Top 10 SSC CGL PYQs to practise first

The questions and kinds of question asked most often come first. Each one says how often and in which papers.

  1. Question 1

    This type asked 22 times: 5 in 2023, 6 in 2024, 11 in 2025. This one: 26 Sep 2025 S2 See all 22 of this type

    74
    In a circle, there is a chord measuring 20 cm that is located 15 cm away from the center. What is the approximate radius of the circle?

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  2. Question 2

    This type asked 13 times: 20 Jul 2023 S1, 20 Jul 2023 S3, 12 Sep 2024 S2, 13 Sep 2024 S2, 23 Sep 2024 S3, 26 Sep 2024 S1, 17 Sep 2025 S3, 18 Sep 2025 S2, 19 Sep 2025 S1, 19 Sep 2025 S3, 23 Sep 2025 S2, 24 Sep 2025 S1, 24 Sep 2025 S2. This one: 24 Sep 2025 S2 See all 13 of this type

    75
    A line is drawn from a point P located 13 cm away from the center O of a circle with radius 5 cm. If the line is tangent to the circle, what is the length of the tangent from point P to the point of contact with the circle?

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  3. Question 3

    This type asked 10 times: 17 Jul 2023 S3, 19 Jul 2023 S4, 27 Jul 2023 S2, 9 Sep 2024 S1, 17 Sep 2024 S2, 23 Sep 2024 S1, 15 Sep 2025 S1, 18 Sep 2025 S3, 19 Sep 2025 S2, 23 Sep 2025 S3. This one: 23 Sep 2025 S3 See all 10 of this type

    71
    Two circles have radii of 8 cm and 3 cm. The distance between their centers is 15 cm. What is the length of a direct common tangent?

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  4. Question 4

    This type asked 9 times: 18 Jul 2023 S1, 24 Jul 2023 S3, 25 Jul 2023 S1, 25 Jul 2023 S3, 26 Jul 2023 S1, 10 Sep 2024 S1, 12 Sep 2024 S1, 16 Sep 2025 S1, 17 Sep 2025 S2. This one: 17 Sep 2025 S2 See all 9 of this type

    70
    A circle with radius xx touches another circle with radius 2x2x externally. What is the length of a direct common tangent?

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  5. Question 5

    This type asked 8 times: 14 Jul 2023 S4, 26 Jul 2023 S1, 24 Sep 2024 S2, 21 Sep 2025 S2, 22 Sep 2025 S3, 23 Sep 2025 S1, 23 Sep 2025 S3, 24 Sep 2025 S2. This one: 24 Sep 2025 S2 See all 8 of this type

    74
    In a circle, chord AB subtends an angle of 60∘60^\circ at the center. What is the angle subtended by the same chord AB at any point C on the major arc (opposite side of the center)?

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  6. Question 6

    Asked 7 times: 10 Sep 2024 S2*, 19 Sep 2024 S2*, 15 Sep 2025 S2*, 18 Sep 2025 S3*, 21 Sep 2025 S2*, 23 Sep 2025 S2*, 24 Sep 2025 S1 (* = numbers or wording changed that year) See all 7 times it was asked

    74
    A circle has a radius of 13 cm. A chord is drawn at a distance of 5 cm from the center. What is the length of the chord?

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  7. Question 7

    Asked 7 times: 18 Jul 2023 S1*, 24 Jul 2023 S3*, 25 Jul 2023 S1*, 25 Jul 2023 S3*, 26 Jul 2023 S1*, 10 Sep 2024 S1*, 12 Sep 2024 S1 (* = numbers or wording changed that year) See all 7 times it was asked

    74
    Two circles C1C_1 and C2C_2 touch each other externally. The radius of C1=16C_1 = 16 cm and the radius of C2=8C_2 = 8 cm. Find the length (in cm) of their common tangent.

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  8. Question 8

    This type asked 6 times: 25 Jul 2023 S1, 10 Sep 2024 S3, 25 Sep 2024 S1, 15 Sep 2025 S1, 18 Sep 2025 S1, 24 Sep 2025 S2. This one: 24 Sep 2025 S2 See all 6 of this type

    71
    The radii of two circles are 6 cm and 2 cm. The centers of the two circles are 10 cm apart. What is the length of a transverse common tangent?

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  9. Question 9

    This type asked 6 times: 19 Jul 2023 S3, 15 Sep 2025 S2, 16 Sep 2025 S1, 16 Sep 2025 S2, 17 Sep 2025 S2, 23 Sep 2025 S1. This one: 23 Sep 2025 S1 See all 6 of this type

    71
    What is the minimum distance between centers of two circles having radii 5 cm and 3 cm such that exactly three common tangents exist?

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  10. Question 10

    This type asked 6 times: 20 Jul 2023 S3, 25 Jul 2023 S2, 9 Sep 2024 S2, 17 Sep 2024 S1, 17 Sep 2025 S3, 19 Sep 2025 S3. This one: 19 Sep 2025 S3 See all 6 of this type

    73
    The angle between two tangents drawn from an external point to a circle is 60∘60^\circ. What is the angle subtended by the chord connecting their points of contact at the center?

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