We are given that a curved road is part of ∘ C, which has a radius of 88 feet. Let's take a look at the given diagram.
To find AB let's recall that if the radius of a circle is perpendicular to a chord, then it bisects the chord and its arc. This means that AE=EB.
Now notice that △ AEC is a right triangle with a hypotenuse AC, which is also a radius of ∘ C. Therefore AC= 88 feet.
To find EC we will use the fact that DC= 88 — as this segment is also a radius — and DE= 15. Notice that by the Segment Addition Postulate the sum of DE and EC is equal to DC.
The length of EC is 73 feet. Let's add this information to our diagram.
Next we can find AE using the Pythagorean Theorem. According to this theorem the sum of the squared legs of a right triangle is equal to its squared hypotenuse.
AE^2+EC^2=AC^2
Let's substitute the appropriate side lengths. Notice that since AE is a side length, we will consider only positive case when taking the square root of AE^2.
