Answer:
12 cm
Explanation:
The rule regarding secants and/or tangents is that the product of distances from their common point to the two intersection points with the circle is the same.
For the tangent the "two" intersection points with the circle are the same point, so ...
product of tangent lengths = product of secant lengths
(8 cm)(8 cm) = (4 cm)(4 cm +x)
Dividing by 4 cm gives ...
16 cm = 4 cm + x
12 cm = x