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Question
In ΔABC, AP ⊥ BC, BQ ⊥ AC. If AP = 7, BQ = 8 and BC = 12, then find AC.
Solution
Given: AP ⊥ BC, BQ ⊥ AC
Now, in ΔAPC and ΔBQC
∠APC ≅ ∠BQC ......[Each equal to 90°]
∠ACP ≅ ∠BCQ .....[Common angle]
∴ By AA criterion of similarity,
ΔAPC ∼ ΔBQC
So, `(AP)/(AC) = (BQ)/(BC)` ......[C.S.S.T.]
Here, AP = 7, BQ = 8, BC = 12
Substituting the values,
`7/(AC) = 8/12`
⇒ AC × 8 = 7 × 12
⇒ AC = `(7 xx 12)/8` = 10.5
Hence, the value of AC is 10.5.
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