Because ∠GAE=∠DAE=90 degrees -∠C=∠GBD.

And ∠GEA and ∠GDB are right angles, so △GEA is similar to △GBD.

In proportion to the corresponding edge:

GE/GD=GA/GB ( 1)

In △GAB and △GED, we can get the following through the equal antipodal angles and the formula (1):

△GAB is similar to △GED (two triangles with proportional sides and equal angles are similar).

So ∠GED=∠GAB

∠DEC=90 degrees -∠GED=90 degrees -∠GAB=∠B

therefore

△CDE is similar to△△△ cab.

Let e be the vertical line of CD and the vertical foot be f,

The corresponding edge of the similar triangles is proportional to the following formula:

DC/AC=EF/BE ( 1)

S triangle ABC = 0.5*AC*BE=9.

S triangle DCE = 0.5*DC*EF= 1.

Divide by two formulas

AC/DC * BE/EF=9

Use (1) instead.

(AC/DC)？ =9

So DC/AC= 1/3.