A property of circular arcs enclosed between intersecting chords and an angle between chords.

If two chords AB and CD are drawn in a circle, and the point of intersection of the chords is point O, then the angle between the chords <AOD = <COB = half the sum of the arc AD and the arc CB.

Such a theorem is proved by considering the angles inscribed in a circle based on the arcs CB and AD. Angle <ABD = half of the AD arc, as an inscribed angle, and resting on the AD arc.
Also <CDB = half of the СВ arc. And the angle <AOD is the outer angle for the triangle OBD, which is equal to the sum of the angles <AOD = (<ABD + <CDB), that is, equal to the half-sum of the arcs AD and BC.

Q.E.D.