In the equilateral triangle, draw in the altitudes of the
triangle and taking the radius of the circle as 1 unit, calculate
the lengths.
In the square it is easiest to take the side of the square as 1
unit and then calculate the radius of the circle.
In the pentagon it is easiest to take the side of the pentagon as 1
unit, and the chord length XZ as x units and then use properties
of similar triangles. Derive a quadratic equation which you can
solve to find x.