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.