Question

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

Answer 1

please see the above pic
u got ur answer

Answer 2

Answer:

Given a triangle ABC. Circle drawn on AB as diameter intersects BC at D. We need to prove that the circle drawn on AC as diameter passes through D.

Join AD.

As AB is a diameter, angle ADB = 90° { angle in a semi-circle }

But angle ADB and angle ADC from a linear pair,

so angle ADC + angle ADB = 180°

angle ADC + 90° = 180°

angle ADC = 180 - 90

= 90°

Since angle ADC = 90°, therefore, the circle drawn on AC as diameter will pass through D.