Answer:
x = 21
Step-by-step explanation:
From the rules of secants (and tangents), you know that ...
x^2 = 7·(7 +56)
x = √(7·63) = √441 = 21
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When secant lines intersect, the product of distances from the point of intersection to the two points on the circle is a constant. The tangent line is a degenerate case where the two points of intersection are the same point (hence the product of distances is x^2). For the other secant, the near distance is 7, and the far distance is 7+56 = 63.
Interestingly, this property holds whether the secants intersect inside the circle or outside (as here). That makes it easier to remember, since there's really only one rule, not three.
