Answer:
CD = 16
Explanation:
We can see that both AC and AB are radii. This means that they are equal, so AC = AB = 17. From segment addition postulate we can say AB = AE + BE
We are given BE, and we found the length of AB, so we can substitute and solve for AE:
AB = AE + BE
17 = AE + 2
AE = 15
Since we are given that AB is perpendicular to CD, ∠AEC would be a right angle, making ΔAEC a right triangle.
Now, we can use the pythagorean theorem to find the length of CE.
a^2 + b^2 = c^2
We are given the hypotenuse, c or AC in this case, and one leg, b, or AE in this case. We can plug in the values we are given:
CE^2 + AE^2 = AC^2
CE^2 + 15^2 = 17^2
CE^2 + 225 = 289
CE^2 = 64
CE = 8
Now, if a chord is perpendicular to a radius(AB in this case) we can say that it is split in half by the radius. This is basically saying that CE = DE = 8.
Again, using segment addition postulate, we can say:
CE + DE = CD
CD = 8 + 8
CD = 16