Question : JKLM is a cyclic quadrilateral in which $\angle \mathrm{K}$ is opposite to $\angle \mathrm{M}$. When $\mathrm{JK}$ and $\mathrm{ML}$ are produced, meet at point $\mathrm{Z}$. $\mathrm{JK}=10 \mathrm{~cm}, \mathrm{KZ}=12 \mathrm{~cm}$ and $\mathrm{MZ}=33 \mathrm{~cm}$. What is the length of $\mathrm{LZ}$?
Option 1: 9 cm
Option 2: 8 cm
Option 3: 10 cm
Option 4: 12 cm
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Correct Answer: 8 cm
Solution :
JKLM is a cyclic quadrilateral in which $\angle$K is opposite to $\angle$M.
When JK and ML are produced, meet at point Z.
JK = 10 cm, KZ = 12 cm, and MZ = 33 cm.
If chords AB and CD of a circle intersect each other at a point P outside the circle then,
PA × PB = PC × PD
Here,
ZK × ZJ = ZL × ZM
⇒ ZL = $12 \times \frac{22}{33}$
⇒ ZL = 8 cm
Hence, the correct answer is 8 cm.
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