10. If circles are drawn taking two sides of a triangle as diameters, prove that the point of intersection of these circl.es lie on the third side.

Construction: Join AD. Proof: Let circle with AB as diameter meets BC at D. Then L ADB = 90°. [Angle in a semicircle] Now L ADB + L ADC = 180° [Linear pair] .. L ADC = 90° 160 As we know angle in a semicircle is 90°, therefore, a circle with AC as diameter passes through D. Hence both the circles meet the third side at D.