In a circle with radius r centered at point O from point A of the circle, two chords are drawn

In a circle with radius r centered at point O from point A of the circle, two chords are drawn, intersecting the circle at points B and C. Find what the angle CAB is equal to if CB = r.

By hypothesis, the chord CB = r. Let us draw the radii of the circle to the edges of the chord CB.

Then in the triangle BОС, OC = ОB = СB = r, therefore, the triangle BОС is equilateral, then the angle COB = OCB = ОВС = 60.

The central angle BOC and the inscribed angle CAB rest on one arc CB, then the inscribed angle is equal to half of the central angle. Angle CAB = BOC / 2 = 60/2 = 30.

Answer: The CAB angle is 30.