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.
Related Questions
Question : In the given figure, the diameter AB and chord CD of a circle meet at P. PT is tangent to the circle at T. If CD = 8 cm, PD = 10 cm, and PB = 8 cm, find AB.
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