Question : In the figure, $\mathrm{XYZ}$ is a secant and $\mathrm{ZT}$ is a tangent to the circle at $\mathrm{T}$. If $\mathrm{TZ}=12$ $\mathrm{cm}$ and $Y Z=8 \mathrm{~cm}$, then find the length of $XY$.
Option 1: 8 cm
Option 2: 9 cm
Option 3: 6 cm
Option 4: 10 cm
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Correct Answer: 10 cm
Solution : According to the question, $ZX \times ZY = ZT^2$ ⇒ $8 \times (YZ + XY) = 12^2$ ⇒ $8 \times (8 + x) = 144$ ⇒ $8 + x = 18$ ⇒ $x = 10$ cm Hence, the correct answer is 10 cm.
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