Points A, B, C are marked on the circle so that AC is the diameter of the circle, the chord BC

Points A, B, C are marked on the circle so that AC is the diameter of the circle, the chord BC is seen from the center of the circle at an angle of 60 °. Find the radius of the circle if AB = √3 cm

Let’s draw our triangle ABC and a circle, because all points of the triangle lie on a circle, which means it is inscribed in a circle.
Constructing an angle from the center to the chord, we get an OCB triangle, in which <C = 60`, OC = OB = R
So the triangle is isosceles with the base BC, and the angles at the base are equal:
<B = <C
Find <B:
<B = (180- <C) / 2 = (180-60) / 2 = 60` = <C
So the triangle is equilateral.
Consider a triangle ABC, angle <C = 60`, and the opposite side AB = √3
Let’s use the sine theorem:
AB / sinC = 2R
R = AB / (2 * sinC) = √3 / (2 * sin 60`) = (√3 * 2) / (2 * √3) = 1 cm
Answer: 1 cm