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Transverse common tangent, square of length = d squared - (r1 + r2) squared (alone or with the direct one)

This type of question, 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. All 7 questions below, oldest first.

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  1. Question 1

    25 Jul 2023 S1

    73
    When two circles of radii r1r_1 and r2r_2 have their centres at a distance d apart, then length of the common transverse tangent is:

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  2. Question 2

    10 Sep 2024 S3

    72
    The radii of two circle are 5 cm and 10 cm and the distance between their centres is 17 cm. Find the length of the transverse common tangent.

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  3. Question 3

    10 Sep 2024 S3

    75
    If the length of a common external tangent to two circles is 9 and that of a common internal tangent is 5, then the product of the radii of the two circles is:

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  4. Question 4

    25 Sep 2024 S1

    59
    The centres of two circles are 36 cm apart. If the radii of these two circles are 15 cm and 9 cm, respectively, then what is the sum of the lengths (in cm) of a direct common tangent and a transverse common tangent of these two circles?

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  5. Question 5

    15 Sep 2025 S1

    73
    The distance between the centers of two circles is dd. The lengths of their direct and transverse common tangents are LL and MM, respectively. If L2+M2=200L^2 + M^2 = 200 and the sum of the squares of their radii is 100, what is the value of dd?

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  6. Question 6

    18 Sep 2025 S1

    70
    A common internal tangent connecting two circles is 9 cm long. The distance between the circles' centers is 15 cm. If the larger circle has a radius of 8 cm, what is the radius of the smaller circle?

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  7. Question 7

    24 Sep 2025 S2

    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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