"Line segments AB and PQ intersect at point O. AP and BQ are perpendiculars to AB. OA = 20 cm, OB = 8 cm, AP = 10 cm. Find the length of BQ."

Q."Line segments AB and PQ intersect at point O. AP and BQ are perpendiculars to AB. OA = 20 cm, OB = 8 cm, AP = 10 cm. Find the length of BQ." (a) 4 cm (b) 6 cm (c) 8 cm (d) None of the above

Answer: A

In triangles AOP and BOQ: \(\angle\)OAP = Alternate angle \(\angle\)OBQ [because AP \(\parallel\) QB] \(\angle\)OPA = \(\angle\)OQB [both are right angles] \(\angle\)AOP = Vertically opposite angle \(\angle\)BOQ ∴ Triangles AOP and BOQ are similar. ∴ \(\cfrac{OA}{AP} = \cfrac{OB}{BQ}\) i.e., \(\cfrac{20}{10} = \cfrac{8}{BQ}\) ⇒ \(BQ = \cfrac{8 \times 10}{20} = 4\) ∴ \(BQ = 4\) cm.