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Math Help - Length of Equal Tangents

  1. #1
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    Length of Equal Tangents

    Two circles of radii 5 cm and 8 cm touch externally. Calculate the length of the common tangent.

    Here Ive attempted it, creating two simultaneous equations for the external point and the centers of each circle. From there i attempted the cosine rule, but to no avail.

    Thanks for help.
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  2. #2
    Master Of Puppets
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    Draw a picture of the circles and the tangent. You should be able to form a right-angled triangle, use pythatogra's thm to solve for the tangent (longest side).
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  3. #3
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    I actually did that the first time. But in using pythagoras, ive got 2 variables each from one circle. So i cannot solve. Unless you can point it out to me on the diagram ill post now.
    Attached Thumbnails Attached Thumbnails Length of Equal Tangents-right-angles.jpg  
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  4. #4
    Master Of Puppets
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    Your picture is not what I had imagined the question to be. Do you know if what you have posted is correct?

    My intepretation was a line that went from the top of one circle to the other. I think the word 'common' is misleading here.
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  5. #5
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    Yes i see what you mean. Thanks for your correction. But just interested is there a way of doing such a question, like the one given in the diagram?
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  6. #6
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    Hello Lukybear
    Quote Originally Posted by Lukybear View Post
    Yes i see what you mean. Thanks for your correction. But just interested is there a way of doing such a question, like the one given in the diagram?
    No. Take a look at the diagram I've attached - which is a modified version of yours.

    Length of Equal Tangents-untitled.jpg

    You'll see that the point where the tangents meet can be anywhere along the vertical line. I've marked the original position as P_1 and shown a second possible position, P_2.

    Grandad
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  7. #7
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    Ok thanks
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