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Math Help - Circles...

  1. #1
    Junior Member whytechocolate01's Avatar
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    Circles...

    Line BC is tangent to point A at C. If AC = 4 and BA = 5, find BC. Please show how to find this. Thanks!
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by whytechocolate01 View Post
    Line BC is tangent to point A at C. If AC = 4 and BA = 5, find BC. Please show how to find this. Thanks!
    is point A the center? if so, it forms a right angle when it intersects with the tangent at the circumference. (this is again, the famous 3-4-5 triangle, we know the answer will be 3, but how to find that for certain?)

    by Pythagoras' theorem:

    (BC)^2 = (AB)^2 - (AC)^2 = 5^2 - 4^2 = 25 - 16 = 9
    => BC = sqrt(9) = 3 ......as expected

    if A is not the center, well, i don't know
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  3. #3
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    A line can be tangent to a circle. Your problem does not match the figure you sent.
    If you consider the context, I would say that A, B ,C are collinear , so BC can be either 9 or 1, depending on the order of the 3 points.
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by alinailiescu View Post
    A line can be tangent to a circle. Your problem does not match the figure you sent.
    If you consider the context, I would say that A, B ,C are collinear , so BC can be either 9 or 1, depending on the order of the 3 points.
    i thought about that, but i decided to go from the diagram and treat the question as a wierd typo.

    was this diagram given whytecholate01? or did you draw it yourself after reading the question?
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  5. #5
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    I think Jhevon is correct

    If BC is a tangent to A that means it = 90 degrees
    we are given the length of two sides therefore pythagoras theorem can be used

    so Jhevon's answer of 3 is correct according to me
    maybe you told him to work out the wrong thing?
    what's point D for?
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  6. #6
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Geometor View Post
    I think Jhevon is correct

    If BC is a tangent to A that means it = 90 degrees
    we are given the length of two sides therefore pythagoras theorem can be used
    assuming A is the center, which is the reasonable assumption we can make i think

    what's point D for?
    it's a decoy to confuse you
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