Observe the given figure:

is the center of the circle ,   and .

The perimeter of the shaded region is sum of , and arc .

From the figure it is observed that is the tangent to the circle at the point and similarly is the tangent to the circle at the point .

From geometrical properties, if two segments from the same exterior point are tangent to a circle, then they are congruent.

Thus, .

From the figure and are the radii of the circle.

Thus, .

As is the combined side of two triangles.

By the Reflexive Property,  .

By SSS Triangle Congruence .

Corresponding parts of congruent triangles are congruent, .

Since , then .

From the figure, .

Thus,    and   .

Sum of three angles in the triangle is .

Use right angle triangle to find .

Substitute   and in the above expression.

.

Since , then .

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Find the arc length of :

Arc length formula: , where is central angle in radians.

Here .

.

Observe the figure, .

Find the radius by using right angle triangle to find .

units.

Therefore, the perimeter of the shaded region   is sum of , and arc .

The perimeter of the shaded region is .

Option E is correct.

Option E is correct.