Thread: [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!

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: .

Hence: .

Therefore: .