In the given figure, QA and PB are perpendiculars to AB. If AO = 10 cm, BO = 6 cm and PB = 9 cm, find AQ.

Let us take OAQ and OBP

∠AOQ = ∠BOP (vertically opposite angles)

∠OAQ = ∠OBP (each 90°)

∴ OAQ ~OBP (by AA similarity criterion)

Given: AO = 10 cm, BO = 6 cm and PB = 9 cm

As, OAQ ~OBP

⇒AQ = 15cm