Answer:
you cut off some of the problem
Step-by-step explanation:
We can see that OW/IG = 5/15 = 1/3 and CW/PG = 7/21 = 1/3. So we have two ratios that result in the same value (1/3). We would need to know if CO/IP is also 1/3 as well, so we can use the SSS similarity theorem. However we don't have that information. So we can't use SSS.
Alternatively, if we knew that angle CWO = angle PGI, then we can use the SAS similarity theorem. But that bit of info isn't given to us, so we can't use SAS either.
AA can't be used because we don't know anything about any pairs of angles.
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In short, the answer is choice D. It cannot be determined. There isn't enough information.
If you want to inscribe a polygon inside a circle, you have a formula that doesn't have to use the apothem. The formula is:
A = (nr²/2)sin(360/n)
Since the polygon is a hexagon, it has 6 sides. Thus, n = 6. Knowing the area, we can determine the radius of the circle, r.
166.28 = (6r²/2)sin(360/6)
r = 8 inches
Thus, the radius of the circle is 8 inches.
