Circles are described on the sides of a triangle as diameters. Prove that the circles on any two sides intersect each other on the third side (or third side produced).

Since,

AB is a diameter


Then,


ADB = 90o (i) (Angle in semi-circle)


Since,’


AC is a diameter


Then,


ADC = 90o (ii) (Angle in semi-circle)


Adding (i) and (ii), we get


ADB + ADC = 90o + 90o


BDC = 180o


Then, BDC is a line


Hence, the circles on any two sides intersect each other on the third side.


24