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Math Help - [SOLVED] Parallelogram. Find quotient.

  1. #1
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    Question [SOLVED] Parallelogram. Find quotient.

    Please help solve the following:

    The point K lies on the side AB of the parallelogram ABCD. The segment DK intersects the diagonal AC at the point O. Find the quotient AO:OC, given that AK=12, KB=6.

    Thank you very much!
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  2. #2
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    Hello, Ivan!

    The point K lies on the side AB of the parallelogram ABCD.
    The segment DK intersects the diagonal AC at the point O.
    Find the quotient AO:OC, given that AK=12, KB=6.
    Code:
          : - - - -  12 - - - - - K - - - 6 - - - :
        A o-----------------------o---------------o B
           \    *               *                  \
            \         *       *                     \
             \              o                        \
              \           * O     *                   \
               \        *               *              \
                \     *                       *         \
                 \  *                               *    \
                D o---------------------------------------o C
                  : - - - - - - - - 18- - - - - - - - - - :

    It can be shown that: . \Delta OAE \sim \Delta OCD

    Hence: . \frac{AO}{OC} \:=\:\frac{AK}{DC} \:=\:\frac{12}{18} \:=\:\frac{2}{3}

    Therefore: . AO:OC \:=\:2:3

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