In trapezoid ABCD on the smaller base BC and on the lateral side of CD, points E and K are taken

In trapezoid ABCD on the smaller base BC and on the lateral side of CD, points E and K are taken, respectively, and point O is marked on the segment AE. Find the ratio AB: BE, if KC = 2, KD = 3, OK || AD, OBA = OBE

Since ABCD is a trapezoid by condition, then AD || BC but OK || AD means OK || and BC;

We can use Thales’ theorem, CK: KD = OE: OA = 2: 3;

BO is a bisector by condition, it means by the property of a bisector: AB: BE = AO: OE = 3: 2;

Answer: AB: BE = 3: 2.