Question 1142858
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For future posts, remember that it will always be helpful for us to try to help you if you tell us HOW you got your answer.<br>
Your answer is not correct; but since we don't know how you got it we can't help you see what you did wrong.<br>
Here is the operating principle for this kind of problem.<br>
Each secant intersects the circle in two places.  The product of the distances from the external point to the two intersection points is the same for both secants.<br>
So in your problem 1 times 2x must be equal to 1 times 4.  That of course means 2x is 4, so x is 2.<br>
Let's look at another more interesting example to help you understand the principle.<br>
Suppose we take the image you provide and change the "1" and "2x" to "2" and "2x" for the upper secant, and change the "1" and "4" for the lower secant to "3" and "9".<br>
Then the distances from the external point to the two intersection points for the lower secant are 3 and 12; the product is 36.<br>
That means the product of "2" and "2+2x" for the upper secant has to be 36 also; that makes 2+2x=18, which leads to x=8.<br>