Question

Two regular polygons are inscribed in the same circle where the first has 1,174 sides and the second has 2,935. If the two polygons have at least one vertex in common, how many vertices in total will coincide?​

Answer 1

vertices in total will coincide = 1174/2 = 587

Explanation:

1st polygon: 1174 sides, 1174 vertex, arc for between 2 vertex= 360°/1174 (arc1)

2nd polygon: 2935 sides, 2935 vertex, arc for between 2 vertex= 360°/2935 (arc2)

360°/1174 = (360°/2935) x (5/2) (every 2.5 arc2 = 1 arc1)

It means every 5 arc2 = 2 arc1, this is the 2nd vertex coincide

vertices in total will coincide = 1174/2 = 587

check: 2935/5 = 587