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Number of common tangents for a given position of circles

This type of question, asked 6 times: 19 Jul 2023 S3, 15 Sep 2025 S2, 16 Sep 2025 S1, 16 Sep 2025 S2, 17 Sep 2025 S2, 23 Sep 2025 S1. All 6 questions below, oldest first.

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  1. Question 1

    19 Jul 2023 S3

    56
    What is the number of common tangents that can be drawn to two circles that touch each other externally?

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  2. Question 2

    15 Sep 2025 S2

    72
    If two circles are touching internally how many common tangents do they have?

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  3. Question 3

    16 Sep 2025 S1

    72
    Two circles intersect at two points. Which of the following statements is true?

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  4. Question 4

    16 Sep 2025 S2

    72
    Three non-overlapping, non-touching circles are drawn in a plane. What is the maximum number of distinct common tangents that can be drawn to them in total?

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  5. Question 5

    17 Sep 2025 S2

    71
    Two circles with radii 6 cm and 2 cm have their centers 10 cm apart. How many common tangents can be drawn between them, and what type(s) of tangents are they?

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  6. Question 6

    23 Sep 2025 S1

    71
    What is the minimum distance between centers of two circles having radii 5 cm and 3 cm such that exactly three common tangents exist?

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