The secant-tangent formula is :
[tex]\frac{\text{Whole Secant}}{\text{ tangent}}=\frac{\text{ tangent}}{\text{ external secant part}}[/tex]
From the problem,
whole secant = (x + 4) cm
tangent = 8 cm
external secant part = 4 cm
Using the formula above :
[tex]\begin{gathered} \frac{x+4}{8}=\frac{8}{4} \\ \text{ cross multiplication :} \\ 4(x+4)=8(8) \\ 4x+16=64 \\ 4x=64-16 \\ 4x=48 \\ x=\frac{48}{4}=12 \end{gathered}[/tex]
ANSWER :
x = 12 cm
