Question

In Figure, ∠BAC = 90° and AD ⊥ BC. Then, ______.

Options

• BD . CD = BC²

• AB . AC = BC²

• BD . CD = AD²

• AB . AC = AD²

Answer 1

In Figure, ∠BAC = 90° and AD ⊥ BC. Then, BD . CD = AD².

Explanation:

From ∆ADB and ∆ADC,

According to the question, we have,

∠D = ∠D = 90°  ...(∵ AD ⊥ BC)

∠DBA = ∠DAC  ...[Each angle = 90° – ∠C]

Using AAA similarity criteria,

∆ADB ∼ ∆ADC

`("BD")/("AD") = ("AD")/("CD")`

BD . CD = AD²