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

`"AC"/"AD" = "AB"/"BD"`  ...(1)

ΔCAB ∼ ΔCDA

`"AC"/"CD" = "AB"/"AD"`  ...(2)

From (1) and (2) we get

`"BD"/"AD" = "AD"/"CD"`

AD² = BD·CD