Segments AB and CD are the diameters of the circle. Prove that the angles BAD, ADC, ABC and BCD are equal.

Consider the triangles formed as a result of the intersection of diameters AB and CD: an isosceles triangle AOD is equal to an isosceles triangle COB on two equal sides, and equal angles between them.

OC = OD = AO = OD, since these segments are the radii of one circle centered at the point O, which divides the diameters AB and CD into two equal parts.

<AOD = <COB, as vertical angles formed at the intersection of two lines AB and CD.

But since the triangles are equal and isosceles, the angles at the base are equal: <BAD = <ADC = <ABC = <BCD.