∴BC*AB=6

Can be seen from the chart

Let b (OA, AB), d (OA/3, AB/3) and c (OA-BC, AB).

Bring points c and d into hyperbola.

(OA-BC)*AB=K →AB*OA-AB*BC=K ②

OA*AB/9=K →AB*OA=9K ③

From ① ② ③

K=3/4