Circles

CBSE Class 10 · Mathematics · 27 past questions

These are the board's own papers. 107 more board questions reprinted in the books we use in class are for signed-in students: sign in.

1. Q1 2026

   In the given figure, PQ and PR are tangents to a circle with centre O and radius 3 cm. If $\angle$ QPR =… (with a figure)

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2. Q2 2026

   In the given figure, PT is a tangent to the circle with centre O and radius r. If $\angle$ POT = 45°, then… (with a figure)

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3. Q3 2026

   Questions number 19 and 20 are Assertion and Reason based questions. Two statements are given, one labelled…

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4. Q4 2026

   In the given figure, TP and TQ are tangents to a circle with centre M, touching another circle with centre N… (with a figure)

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5. Q5 Sample paper 2026-27

   Prove that the parallelogram circumscribing a circle is a rhombus.

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6. Q6 Sample paper 2026-27

   In a technology park in Hyderabad, a company installed a circular meditation garden for its employees as… (with a figure)

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7. Q7 2025

   At point A on the diameter AB of a circle of radius 10 cm, tangent XAY is drawn to the circle. Find the… (with a figure)

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8. Q8 2025

   If tangents PA and PB drawn from an external point P to the circle with centre O are inclined to each other… (with a figure)

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9. Q9 2025

   Questions number 19 and 20 are Assertion and Reason based questions. Two statements are given, one labelled…

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10. Q10 2025

    In the given figure, PC is a tangent to the circle at C. AOB is the diameter which when extended meets the… (with a figure)

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11. Q11 2025

    The tangents drawn at the extremities of the diameter of a circle are always…

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12. Q12 2025

    In the given figure, PA is a tangent from an external point P to a circle with centre O. If $\angle$ POB =… (with a figure)

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13. Q13 2025

    A person is standing at P outside a circular ground at a distance of 26 m from the centre of the ground. He… (with a figure)

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14. Q14 2025 (Basic)

    In the given figure, PA is a tangent to a circle with centre O. If OP = 10 cm, then the length of AP is… (with a figure)

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15. Q15 2025 (Basic)

    Two concentric circles are of radii 6 cm and 10 cm. Find the length of the chord of the larger circle which…

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16. Q16 2024

    Maximum number of common tangents that can be drawn to two circles intersecting at two distinct points is…

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17. Q17 2024

    In the given figure, if PT is a tangent to a circle with centre O and $\angle$TPO = 35°, then the measure of… (with a figure)

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18. Q18 2024

    In the given figure, O is the centre of the circle. MN is the chord and the tangent ML at point M makes an… (with a figure)

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19. Q19 2024

    In the given figure, tangents PA and PB to the circle centred at O, from point P are perpendicular to each… (with a figure)

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20. Q20 2023

    Questions number 19 and 20 are Assertion and Reason based questions carrying 1 mark each. Two statements are…

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21. Q21 2023

    In the given figure, O is the centre of the circle. AB and AC are tangents drawn to the circle from point A.… (with a figure)

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22. Q22 2023

    In the given figure, TA is a tangent to the circle with centre O such that OT = 4 cm, $\angle$OTA =… (with a figure)

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23. Q23 2023

    Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which…

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24. Q24 2023

    The discus throw is an event in which an athlete attempts to throw a discus. The athlete spins anti-clockwise… (with a figure)

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25. Q25 2023 (Basic)

    The distance between two parallel tangents of a circle of diameter 7 cm is…

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26. Q26 2023 (Basic)

    (Assertion – Reason based questions)…

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27. Q27 2022

    Two concentric circles are of radii 4 cm and 3 cm. Find the length of the chord of the larger circle which…

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