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Direct common tangent of two separate circles, square of length = d squared - (r1 - r2) squared: find length, distance or a radius

This type of question, 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. All 10 questions below, oldest first.

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  1. Question 1

    17 Jul 2023 S3

    64
    The distance between the centres of two circles having radii 16 cm and 8 cm, is 26 cm. The length (in cm) of the direct common tangent of the two circles is:

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  2. Question 2

    19 Jul 2023 S4

    73
    The distance between the centres of two circles of radii 2 cm and 6 cm is 5 cm. Find the length of the direct common tangent.

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  3. Question 3

    27 Jul 2023 S2

    72
    The distance between the centres of two circles having radii 22 cm and 18 cm, is 32 cm. The length (in cm) of the direct common tangent of the two circles is :

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  4. Question 4

    9 Sep 2024 S1

    67
    The distance between the centres of two circles of radii 2222 cm and 1010 cm is 3737 cm. If the points of contact of a direct common tangent to these circles are M and Q, then find the length of the line segment MQ.

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  5. Question 5

    17 Sep 2024 S2

    54
    M and N are, respectively, the centres of two circles of radii 12 cm and 8 cm. QR is the common tangent to the circles. If MN = 16 cm, then what will be the length of QR?

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  6. Question 6

    23 Sep 2024 S1

    61
    For two circles of radius 7 units and 72\frac{7}{2} units, whose centres are 15 units apart, what is the length of the direct common tangent in units? (Correct to 3 decimal places.)

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  7. Question 7

    15 Sep 2025 S1

    72
    Two circles have radii of 12 cm and 4 cm. If the length of a direct common tangent is 15 cm, what is the distance between their centers?

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  8. Question 8

    18 Sep 2025 S3

    70
    Two circles have radii in the ratio 2:12 : 1. The length of a direct common tangent is 8 cm8 \text{ cm}, and the distance between their centers is 10 cm10 \text{ cm}. What is the radius of the smaller circle?

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  9. Question 9

    19 Sep 2025 S2

    70
    Two circles, with radii of r1r_1 and r2r_2 respectively, have their centers separated by a distance of dd. If the length of a direct common tangent is equal to the distance between the centers, which of the following is true?

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  10. Question 10

    23 Sep 2025 S3

    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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