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Question
Using Pythagoras theorem determine the length of AD in terms of b and c shown in Figure.
Solution
We have,
In ΔBAC, by Pythagoras theorem
BC2 = AB2 + AC2
⇒ BC2 = c2 + b2
⇒ BC = `sqrt(c^2+b^2)` ........(i)
In ΔABD and ΔCBA
∠B = ∠B [Common]
∠ADB = ∠BAC [Each 90°]
Then, ΔABD ~ ΔCBA [By AA similarity]
`therefore"AB"/"CB"="AD"/"CA"` [Corresponding parts of similar Δ are proportional]
`rArrc/sqrt(c^2+b^2)="AD"/b`
`rArr"AD"="bc"/sqrt(c^2+b^2)`
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