Two right triangles ABC and DBC are drawn on the same hypotenuse

• Geometry (C10)

Two right triangles ABC and DBC are drawn on the same hypotenuse BC and on the same side of BC. If AC and BD intersect at P, prove that AP × PC = BP × DP.

Answer

∆APB ~ ∆DPC (AA similarity)

AP/DP = BP/PC

⇒ AP × PC = BP × DP