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

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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 = 15 cm

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