Question

17 in ∆abc,angle adb= 90°
prove that AB^2 =AC^2+BC^2-2BC*CD​

Answer 1

Answer:

This can be proved in various ways. Let me try one,

Refer following figure,

Refer triangle, △ABD

tanθ=ADBD(1)

Refer triangle △ACD ,

tan(90−θ)=ADCD

cotθ=ADCD(2)

Multiplying (1),(2)⟹

tanθ×cotθ=ADBD×ADCD=1

AD2=BD×CD■

Refer following figure

In △ABC, if ∠ABC=θ , ∠ACB=(90−θ)

∴ in △ACD,∠CAD=90−(90−θ)=θ

Refer triangle, △ABD

tanθ=ADBD(1)

Refer △ACD ,

tanθ=CDAD(2)

Equating (1),(2)⟹

tanθ=ADBD=CDAD

AD2=BD×CD■

Step-by-step explanation:

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