Math, asked by ktanuj1432, 3 months ago


In ∆ABC angle BAC= 90°, AD is perpendicular to BC. Prove that AD/BD= AD/CD= BD×CD​

Answers

Answered by emily1532
1

Answer:

In △ABC, if ∠ABC=θ, ∠ACB=(90−θ)

∴ in △ACD,∠CAD=90−(90−θ)=θ

Refer triangle, △ABD

tanθ=AD/BD-----(1)

Refer △ACD,

tanθ=CD/AD-----(2)

Equating (1),(2)⟹ Tanθ=AD/BD=CD/AD

AD²=BD×CD

Hence proved!

hope this helps!

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