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Math Help - geometry length

  1. #1
    Member helloying's Avatar
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    geometry length

    help me help me. i don understand
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  2. #2
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    Quote Originally Posted by helloying View Post
    help me help me. i don understand
    I've marked equal distances by the same colour.

    In my opinion there is missing an additional property of this triangle: Radius r or the height of the triangle or ...
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  3. #3
    Member helloying's Avatar
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    oh i see but why are they equal? wat is the property that makes them equal?
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  4. #4
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    Quote Originally Posted by helloying View Post
    oh i see but why are they equal? wat is the property that makes them equal?
    The red lines and the blue lines are tangent lines to a circle.

    The complete figur (=circle + tangents) is symmetric to the line MP, if P denotes the point of intersection of the 2 tangent lines.
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  5. #5
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    I found a way to get an answer in terms of r, but I am not sure that we shouldn't be able to deduce r somehow and I suspect Earboth knows what I'm about to post already, but just in case:

    geometry length-triangleint.jpg

    Angles marked the same are the same because of congruent triangles.
    2\times +2\circ+2\square = 2\pi
    \times+\circ+\square = \pi
    \tan(\times) = 25/r
    \tan(\circ) = 12/r
    <br />
\tan(\square) = \tan(\pi-\circ-\times)
    =-\tan(\circ+\times)
    <br />
=-\frac{(25/r)+(12/r)}{1-300/r^2}
    =\frac{37r}{300-r^2}
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  6. #6
    Member helloying's Avatar
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    by the way i think i may have missed out a important property. P is the centre of the line CB. My picture is not very accurate. Is this important to know to solve the length?
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  7. #7
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    Quote Originally Posted by helloying View Post
    by the way i think i may have missed out a important property. P is the centre of the line CB. My picture is not very accurate. Is this important to know to solve the length? Yes
    If P is the midpoint of BC then PB = 12 too and - most important - RB = 12 for symmetry reasons.

    You now can determine the lengths of all sides:

    AC= 25 + 12 = 37
    BC = 12 + 12 = 24
    AB = 25 + 12 = 37

    That means you are dealing with an isosceles triangle with base BC = 24
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