Question

2. In the given figure, angle BAC = 90° and AD perpendicular BC. Then
A)BC.CD = BC
B)AB.AC =BO
C) BC.CD = AD
D)AB.AC = AD
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Answer 1

Correct question

In the given figure, angle BAC = 90° and AD perpendicular BC. Then,

A)BC.CD = BC²

B)AB.AC =BC²

C) BD.CD = AD²

D)AB.AC = AD²

Answer:

Option C) BD.CD = AD²

Explanation:

Given that, In ∆ABC angle BAC = 90° and AD is perpendicular to BC.

A perpendicular to AD such that angle ADB and angle ADC = 90°.

In ∆ADB and ∆ADC

→ ∠BAD = ∠ACD

( In ∆ADC by angle sum property

∠ADC + ∠DAC + ∠ACD = 180°

90° + ∠DAC + ∠ACD = 180°

∠DAC + ∠ACD = 90° ----(1)

Also, ∠BAD + ∠DAC = 90° ----(2)

From (eq 1) & (eq 2) we get

∠BAD = ∠ACD )

→ ∠ADB = ∠ADC (both of 90°)

By AA

∆ADB ~ ∆ADC

Since, ∆ADB and ∆ADC are similar then their corresponding sides are equal.

⇒ AD/BD = DC/AD

Cross-multiply them

⇒ AD(AD) = BD(DC)

⇒ AD² = BD.DC

Answer 2

Step-by-step explanation:

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