Col. A: \(\frac{ BD}{AB }\)
Col. B: \(\frac{BC}{DC }\)

Cross-multiplying the denominators:

Col. A: \((BD)(DC)\)
Col. B: \((BC)(AB)\)

We know, in △BDC:
\(BC^2 = BD^2 + CD^2\); i.e. BC > BD and also BC > CD

In △BDA:
\(AB^2 = BD^2 + AD^2\); i.e. AB > BD and AB > AD

Compare BD and AB: BD < AB
Compare DC and BC: DC < BC

Col. A < Col. B
Hence, option B