# Thread: [SOLVED] Parallelogram. Find quotient.

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

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!

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