Answer:
12 cm
Explanation:
You want to know the length b of one secant in the diagram with two secants and their lengths shown.
Secant relation
The product of lengths from the common point to the two intersections with the circle is the same for both secants.
6·b = 4·18
b = 4·18/6 = 12 . . . . cm
The length of segment b is 12 cm.
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Additional comment
The same is true for a tangent. In that case, the two points of intersection are the same point, so the length is squared.
When the segments intersect inside the circle, so are chords instead of secants, the same relation holds. The product of distances from the common point of the chords to the circle is the same for both chords.
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