9514 1404 393
Answer:
C) 4
Step-by-step explanation:
We observe that the top segments are in the same 3:4 ratio as the bottom segments. This means they are the same lengths: 3x = 12, 4x = 16. Either of these equations tells us x = 4.
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Additional comment
In case you aren't convinced, you can solve this using the secant rule for segments and circles: the product of the lengths to the circle intercepts are the same for both secants.
12(12 +16) = 3x(3x +4x)
336 = 21x² . . . . . simplify
16 = x² . . . . . . . . divide by 21
4 = x . . . . . . . . . .positive square root
