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

The diagram is-

Join AB.
∠ ABD = 90° (Angle in a semicircle)
∠ ABC = 90° (Angle in a semicircle)
So, ∠ ABD + ∠ ABC = 90° + 90° = 180°
Therefore, DBC is a line.

Hence the point of intersection of two circles lie on the third side.