A point D is taken from the side BC of a right-angled triangle

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A point D is taken from the side BC of a right-angled triangle ABC, where AB is hypotenuse. Then

1. AB² + CD² = BC² + AD²
2. CD² + BD² = 2AD²
3. AB² + AC² = 2AD²
4. AB² = AD² + BD²

Correct Option: A

As per the given in question , we draw a figure right-angled triangle ACB

In ∆ABC, AC² + BC² = AB²
In ∆ACD, AD² = AC² + CD²
⇒ AD² – CD² = AC²
∴ AB² + AC² = AC² + BC² + AD² – CD²
⇒ AB² = BC² + AD² – CD²
⇒ AB² + CD² = BC² + AD²