In △ABC, ∠B is a right angle. If D is the foot of the perpendicular drawn from B on AC, then:

1. BC² + CD² = AC²

2. AB² - BC² = AD² - CD²

3. BC² - BD² = AB² - AD²

4. None of these.

In △ ADB,

Using Pythagoras theorem,

Hypotenuse² = Base² + Height²

⇒ AB² = BD² + AD²

⇒ BD² = AB² - AD² …..(1)

In △ BDC,

Using Pythagoras theorem,

⇒ BC² = BD² + CD²

⇒ BD² = BC² - CD² ……(2)

Equating eq.(1) and (2), we get:

⇒ AB² - AD² = BC² - CD²

⇒ AB² - BC² = AD² - CD².

Hence, option 2 is the correct option.