Cyclic Ratio-Arc All Integer Polygons Abstract In the 2013 work [3], the author discussed the conditions for the side lengths of a cyclic quadrilateral with all integer sides, where one adjacent angle is n times the other. In 2023, [5] utilized Chebyshev polynomials of the second kind and a multiple-angle construction method to discuss building Brahmagupta n-gons on the unit circle with rational side lengths, which were then scaled to positive integers. In the 2025 work [4], the authors explored the case of a triangle where two adjacent angles are in the ratio M:N, having integer sides and further where the area is also an integer. Our work generalizes these previous results. We have found the conditions for cyclic polygons where the angles are in integer ratios, and the side lengths, diagonals, and area are all integers. The results from works [3], [4], and [5] become special cases within our broader framework, and upon examination, our results are consistent with theirs. The primary reason previous results could not be generalized to polygons lies in our introduction of the multiple-arc concept. By applying Chebyshev polynomials of the second kind and the modified Vieta–Fibonacci polynomials, we express all sides and all diagonals of the all-integer polygon as Vieta–Fibonacci modified polynomials. Furthermore, we derived the formulation for the multiple-arc perfect polygon.