PYQ Vault

Circles touching externally: direct common tangent = 2 x square root of r1 r2

This type of question, 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. All 9 questions below, oldest first.

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  1. Question 1

    18 Jul 2023 S1

    75
    Two circles of radii 10 cm and 5 cm touch each other externally at a point A. PQ is the direct common tangent of those two circles of centres O1O_1 and O2O_2, respectively. The length of PQ is equal to:

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  2. Question 2

    24 Jul 2023 S3

    54
    Two circles with radii 22 cm and 16 cm touch each other externally. The length of the direct common tangent is:

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  3. Question 3

    25 Jul 2023 S1

    64
    In the following figure, there are two circles that touch each other externally. The radius of the first circle with centre P is 25 cm. The radius of the second circle with centre Q is 4 cm. Find the length of their direct common tangent AB.

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  4. Question 4

    25 Jul 2023 S3

    67
    Two circles touch each other externally. The radius of the first circle with centre O is 6 cm. The radius of the second circle with centre P is 3 cm. Find the length of their common tangent AB.

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  5. Question 5

    26 Jul 2023 S1

    52
    There are two circles that touch each other externally. Radius of the first circle with centre O is 12 cm. Radius of the second circle with centre A is 8 cm. Find the length of their common tangent BC.

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  6. Question 6

    10 Sep 2024 S1

    59
    Two circles of radii 18 cm and 12 cm touch each other externally. Find the length (in cm) of their direct common tangent.

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  7. Question 7

    12 Sep 2024 S1

    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

    16 Sep 2025 S1

    73
    Two circles with radii r1r_1 and r2r_2 touch each other externally. If the length of their direct common tangent is TT, which of the following is the correct relationship between TT, r1r_1, and r2r_2?

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  9. Question 9

    17 Sep 2025 S2

    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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