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.

Explanation

In `DeltaCPA` and `DeltaCQB`,
`/_CPA~=/_CQB`…(Each measures `90^(@)`)
`/_ACP~=/_BCQ` …..(Common angle)
`:.DeltaCPA~DeltaCQB` ……….(AA test similarity)
`:.(AP)/(BQ)=(AC)/(BC)`……[Corresponding sides of similar triangles are in proportion]
`:.7/8=(AC)/12`
`:.ACxx8=7xx12`
`:.AC=10.5`
`AC=10.5`