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
Answer (1)
25th Jan, 2024
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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