Find the measure of AB¯¯¯¯¯¯¯¯. A. 14 B. 22 C. 21 D. 20

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

A geometric proof is a step-by-step explanation that uses definitions, axioms, postulates, and previously proved theorems to draw a conclusion about a geometric statement. You're given something in the beginning (It's called "Given" That's how you'll address it when proving.) and you prove that's it's either correct or incorrect. 

Hope this helps. :3