Please help its important!! Triangle ABC in the figure above represents the area serviced by a shipping company that plans to build a distribution center at the incenter of the triangle located at point E. A circle is constructed to represent the location of the center. The diameter of the circle is 28 miles. The existing road is perpendicular to the incenter and the company is looking to build 2 more perpendicular roads but connecting the other 2 sides of the triangle. How many more miles of road will be needed?

Select one:
A. 28
B. 34
C. 43
D. 56

A. 28

Step-by-step explanation:

A. 28

step 1.

We know that the diameter of the circle inscribed within the triangle is 28 miles, and we know that E is the incenter of triangle ABC.

step 2.

Next, we learned that the perpendicular legs from the incenter to the sides of the triangle are congruent, and we know that the radius of a circle is 1/2 of the diameter of the circle.

step 3.

Since the diameter of the circle is 28, we know the distance of segment DE is 14. Next, we know the perpendicular legs are equal to segment DE. Thus, we can solve for the amount of additional miles of road by writing 14 + 14 = 28.