AC and BD are diameters of one circle with center O Prove that AB is parallel to CD.

Connect points A, B, C, D (ends of diameters). We get a quadrilateral with diagonals AC and BD, which intersect at point O.

Consider the triangle ABC.

∠ABС = 90 °, as an inscribed angle in a circle, based on the diameter of the AC.

∠ADC = 90 °, also based on the AC diameter.

Similarly, we obtain ∠BCD = ∠BAD = 90 °, as the angles inscribed in a circle based on the diameter BD.

ABCD is a quadrangle with all angles straight, i.e. ABCD is a rectangle.

This means that its opposite sides are parallel, that is, AB || CD and AD || BC.