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Question
In the given figure, ∠ABC = 90° and BD⊥AC. If BD = 8cm, AD = 4cm, find CD.
Solution
It is given that ABC is a right angled triangle
and BD is the altitude drawn from the right angle to the hypotenuse.
In Δ DBA and Δ DCB, we have :
∠𝐵𝐷𝐴= ∠𝐶𝐷𝐵
∠𝐷𝐵𝐴= ∠𝐷𝐶𝐵=90°
Therefore, by AA similarity theorem, we get :
ΔDBA - Δ DCB
⇒ `(BD)/(CD)=(AD)/(BD)`
⇒ `CD=(BD^2)/(AD)`
`CD = (8xx8)/4=16 cm`
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