Answer:
x = 36
Explanation:
Given a tangent segment of length 24, and a secant segment from the same point with an external length of 12 and a total length of (12+x), you want to find the value of x.
Relation
The product of lengths from the common point to the two intersections with the circle are the same for both segments. In the case of the tangent, the two intersections with the circle are the same point, so the square of the length is used.
24² = 12(12 +x)
2·24 = 12 +x . . . . . . . divide by 12
36 = x . . . . . . . . . subtract 12
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