(I'm Overwhelmed) Geometry Progress Quiz #10 Q3

Hey everyone!

I thought that the answer to this question here is 5 and not 7.

I first tried to solve it using the logic of a 30-60-90 triangle, and then later used trigonometry to figure it out. Do let me know in case I am missing something. Thanks!

They’re asking when the radius of the circle exceeds the side length of a regular polygon.

As you have shown AF = 2 \cdot (2 \cos (54^{\circ})) > 2 = r then this can’t possibly work

Thanks! I tend to misread quant questions all the time lol.