Question

In the following figure, ∠ABC = 90° and BD ⊥ AC. If BD = 8 cm and AD = 4 cm, find CD.

In the following figure, ∠ABC = 90° and BD ⊥ AC. If BD = 8 cm and AD = 4 cm, find CD.

Answer 1

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) and (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