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In DeltaABC, AP |BC, BQ|AC. B-P-C,A-Q-C,...

In `DeltaABC, AP _|_BC, BQ_|_AC. B-P-C,A-Q-C,`
then prove that `DeltaCPA~DeltaCQB`.
If `AP=7, BQ=8, BC=12` then find AC.

Text Solution

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In `DeltaCPA` and `DeltaCQB`,
`/_CPA~=/_CQB` …..(Each of measure `90^(@)`)
`/_ACP~=/_BCQ`……..(Common angle)
`:.DeltaCPA~DeltaCQB` …….. ("AA" test of similarity)
`:.(AP)/(BQ)=(AC)/(BC)` ……..(Corresponding sides of similar triangles are proportional)
`:.(7)/(8)=(AC)/(12)`.........(Substituting the given values)
`:.ACxx8=7xx12`
`:.AC=10.5`
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