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Difficult

From Inscribed Angles to Sector Area

GMAT-L1LNTA

An inscribed angle on a circle with radius $4$ has an angle measure of $ \theta $degrees.

Now, assume this circle also has a central angle that intercepts the same arc as that of the inscribed angle. In terms of $ \theta $, what is the area of the sector outlined by the central angle?

A

$\cfrac{4π}{45}$

B

$\cfrac{8π}{45}$

C

$\cfrac{2\thetaπ}{45}$

D

$\cfrac{4\theta π}{45}$

E

$\cfrac{8\thetaπ}{45}$