In the figure, AB is common chord of the two circles. If AC and AD are diameters; prove that D, B and C are in a straight line. O₁ and O₂ are the centers of two circles.

We know that,

Angle in a semi-circle is a right angle.

∴ ∠DBA = ∠CBA = 90°

Adding both we get,

⇒ ∠DBA + ∠CBA = 180°

Hence proved that, D, B and C form a straight line.