# In ΔABC AD⊥BC and AD²=BD.DC. The measure of ∠BAC is:

- 90
^{o} - 45
^{o} - 60
^{o} - 75
^{o}

Correct option is** (1) 90° **

**Explanation:- **In Δ ABC,

AD⊥ BC and AD² = BD. DC (Given in the question)

In Δ ADB,

AB² + AD² + BD² ……………………. (1)

In Δ ACD,

AC² = AD² + CD²

Add equation (1) and (2),

AB² + AC² = AD² + AD² + BD² + CD²

AB² + AC² = 2. AD² + BD² + CD²

AB² + AC² = 2. BD. CD + BD² + CD² {AD² = BD. DC (Given)}

= (BD + CD)² {(a + b)² = a² + b² + 2ab}

AB² + AC² = BC²

So, Δ ABC is a right triangle and right triangle at A.

Then, the ∠BAC = 90°

Hence, the answer is (1) 90°.