In the given figure, we find : 1. BD AB 2. BD AB 3. BD = AB 4. DC AB

In △ ABC, By angle sum property of triangle, ⇒ ∠A + ∠B + ∠C = 180° ⇒ ∠A + 75° + 35° = 180° ⇒ ∠A + 110° = 180° ⇒ ∠A = 180° - 110° = 70°. From figure, AD bisects angle A. ∴ ∠BAD = ∠DAC = = 35°. In △ ABD, By angle sum property of triangle, ⇒ ∠ABD + ∠BAD + ∠ADB = 180° ⇒ 75° + 35° + ∠ADB = 180° ⇒ ∠ADB + 110° = 180° ⇒ ∠ADB = 180° - 110° = 70°. Since, ∠BAD ∠ADB ∴ BD AB (If two angles of a triangle are unequal, the greater angle has the greater side opposite to it.) Hence, Option 2 is the correct option.