Answer:
C. 21
Step-by-step explanation:
We use the Power of Point theorem, which states that for points A, B, C, D, and E oriented in the way shown in the attachment:
BC * AC = DC * EC
Here:
AC = AB + BC = (2x + 5) + 9 = 2x + 14
BC = 9
DC = 10
EC = KC = (1 + 2x) + 10 = 2x + 11
So plug all these in:
BC * AC = DC * EC
9 * (2x + 14) = 10 * (2x + 11)
18x + 126 = 20x + 110
2x = 126 - 110 = 16
x = 8
Put this back into the expression for AB:
AB = 2x + 5 = 2 * 8 + 5 = 16 + 5 = 21
The answer is thus C.
~ an aesthetics lover
