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Question
In the following Figure, ∠ABC = 90° and BD ⊥ AC. If BD = 8 cm and AD = 4 cm, find CD.
Solution
We have, ∠ABC = 90° and BD ⊥ AC
Now, ∠ABD + ∠DBC − 90° …(i) [∵ ∠ABC − 90°]
And, ∠C + ∠DBC − 90° …(ii) [By angle sum prop. in ΔBCD]
Compare equations (i) & (ii)
∠ABD = ∠C …(iii)
In ΔABD and ΔBCD
∠ABD = ∠C [From (iii)]
∠ADB = ∠BDC [Each 90°]
Then, ΔABD ~ ΔBCD [By AA similarity]
`therefore"BD"/"CD"="AD"/"BD"` [Corresponding parts of similar Δ are proportional]
`rArr8/"CD"=4/8`
`rArr"CD"=(8xx8)/4=16` cm
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