Question

In the adjacent figure ∠BAC = 90° and AD ⊥ BC then
 

Options

• BD.CD = BC²  

• AB.AC = BC²  

• BD.CD = AD²  

• AB.AC = AD² 

Answer 1

BD.CD = AD²

Explanation;

Hint:

ΔBAC ∼ ΔBDA

${\displaystyle \frac{\text{AC}}{\text{AD}}=\frac{\text{AB}}{\text{BD}}}$  ...(1)

ΔCAB ∼ ΔCDA

${\displaystyle \frac{\text{AC}}{\text{CD}}=\frac{\text{AB}}{\text{AD}}}$  ...(2)

From (1) and (2) we get

${\displaystyle \frac{\text{BD}}{\text{AD}}=\frac{\text{AD}}{\text{CD}}}$

AD² = BD·CD