Secant and tangent theorem: Square of measure of tangent is equal to the product of length of whole secant and length of exterior secant segment, i.e.
[tex] \text{ tangent }^2=\text{whole secant}\cdot \text{exterior secant} [/tex].
The whole secant wuth exterior secant 4 cm is 4+x cm. Tangent is 7 cm. Using previous theorem, you can get that
[tex] 7^2=(4+x)\cdot 4 [/tex].
Solve this equation:
[tex] 49=16+4x,\\ 4x=49-16,\\ 4x=33,\\ x=8.25\approx 8.3 [/tex] cm.
Answer: x=8.3 cm.
