In ∆ ABC, AD ⊥ BC and AD² = BD.DC. The measure

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In ∆ ABC, AD ⊥ BC and AD² = BD.DC. The measure of ⊥BAC is:

1. 60°
2. 75°
3. 90°
4. 45°

Correct Option: C

According to question , we draw a figure triangle ABC

In right angled ∆ ABD and ∆ ADC,
AB² = AD² + BD² and, AC² = AD² + DC²
On adding, we get
AB² + AC² = 2AD² + BD² + CD²
⇒ AB² + AC² = 2BD × CD + BD² + CD²
[∵ AD² = BD × CD]
⇒ AB² + AC² = (BD + CD)² = BC²
∆ ∠BAC = 90°