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Two circles touching externally with given radii: length of the direct common tangent

The same question, asked 7 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. Every wording 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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