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Radius, half-chord and distance from the centre form a right triangle: find any one

This type of question, asked 22 times: 14 Jul 2023 S2, 14 Jul 2023 S4, 17 Jul 2023 S1, 20 Jul 2023 S4, 24 Jul 2023 S1, 10 Sep 2024 S2, 13 Sep 2024 S2, 18 Sep 2024 S1, 19 Sep 2024 S2, 23 Sep 2024 S3, 24 Sep 2024 S1, 15 Sep 2025 S2, 17 Sep 2025 S2, 18 Sep 2025 S3, 19 Sep 2025 S2, 20 Sep 2025 S1, 21 Sep 2025 S2, 22 Sep 2025 S1, 23 Sep 2025 S2, 24 Sep 2025 S1, 24 Sep 2025 S2, 26 Sep 2025 S2. All 22 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    14 Jul 2023 S2

    71
    A 15 cm long perpendicular is drawn from the centre of a circle to its 40 cm long chord. Find the radius of the circle.

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  2. Question 2

    14 Jul 2023 S4

    64
    In a circle, a 14 cm long chord is at 24 cm from the centre of the circle. Find the length of the radius of the circle.

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  3. Question 3

    17 Jul 2023 S1

    68
    If the area of a circle is 616 cm2616\ \text{cm}^2 and a chord XY = 10 cm, then find the perpendicular distance from the center of the circle to the chord XY.

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  4. Question 4

    20 Jul 2023 S4

    59
    A 15 cm long perpendicular is drawn from the centre of a circle to a 40 cm long chord. Find the diameter of the circle.

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  5. Question 5

    24 Jul 2023 S1

    61
    If the length of a chord, drawn at a distance of 21 cm from the centre of a circle, is 40 cm, then the radius (in cm) of the circle is:

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  6. Question 6

    10 Sep 2024 S2

    73
    In a circle of radius 5135\sqrt{13} cm, a chord is at a distance of 10 cm from the centre of the circle. Find the length (in cm) of the chord.

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  7. Question 7

    13 Sep 2024 S2

    68
    A circle's centre is connected to its 50 cm long chord by a perpendicular that is 21 cm long. Find the circle's radius.

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  8. Question 8

    18 Sep 2024 S1

    75
    A chord of length 32 cm is drawn at a distance of 12 cm from the centre of a circle. Find the radius of the circle.

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  9. Question 9

    19 Sep 2024 S2

    66
    The radius of the circle is 10 cm and the perpendicular distance from the chord to the centre is 6 cm. The length of the chord is:

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  10. Question 10

    23 Sep 2024 S3

    53
    If in a circle a chord of length 14 cm is at a distance of 24 cm from its centre, then the length of the radius of the circle is:

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  11. Question 11

    24 Sep 2024 S1

    60
    The radius of a circle is 12.5 cm and the length of one its chords is 11 cm. What is the distance of the chord from the centre? (correct to one decimal place)

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  12. Question 12

    15 Sep 2025 S2

    73
    Two chords, AB and CD, are equal in length and are at a distance of 10 cm from the center of a circle. If the radius is 26 cm, what is the length of AB?

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  13. Question 13

    17 Sep 2025 S2

    73
    In a circle, a chord AB is 12 cm long and is at a distance of 4 cm from the center. What is the radius of the circle?

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  14. Question 14

    18 Sep 2025 S3

    71
    In a circle having a radius 10 cm, a chord is 6 cm away from the center. Find the length of the chord.

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  15. Question 15

    19 Sep 2025 S2

    71
    A chord of a circle has a length of 2212\sqrt{21} cm. The distance of the chord from the center is 5 cm. What is the radius of the circle?

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  16. Question 16

    20 Sep 2025 S1

    72
    A circle that has a radius of 5 centimeters, and there is a chord measuring 8 centimeters in length. What is the distance from the center of the circle to the chord?

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  17. Question 17

    21 Sep 2025 S2

    72
    The line segment from the center of a circle to the midpoint of a chord is 10 cm long. If the radius is 26 cm, what is the length of the chord?

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  18. Question 18

    22 Sep 2025 S1

    72
    A chord of length 24 cm lies 7 cm away from the center of a circle. What is the approximate radius of the circle?

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  19. Question 19

    23 Sep 2025 S2

    74
    A chord is drawn in a circle with a radius of 15 cm. If the distance of the chord from the center is 9 cm, what is the length of the chord?

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  20. Question 20

    24 Sep 2025 S1

    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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  21. Question 21

    24 Sep 2025 S2

    73
    A circle with a radius of 20 cm. A chord of length 32 cm is drawn. What is the distance from the center of the circle to the chord?

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  22. Question 22

    26 Sep 2025 S2

    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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