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Two circles $\mathrm{C_{1}}$ and $\mathrm{C_{2}}$ intersect at two distinct points $\mathrm{A}$ and $\mathrm{B}$ in a plane. Let a line passing through $\mathrm{A}$ meet the circle $\mathrm{C}_{1}$ and $\mathrm{C}_{2}$ in $\mathrm{X}$ and $\mathrm{Y}$ respectively. Let $\mathrm{P}$ be the mid point of $\mathrm{XY}$ and $\mathrm{PQ}$ meet the circles $\mathrm{C}_{1}$ and $\mathrm{C}_{2}$ in $\mathrm{Q}$ and $\mathrm{Z}$ respectively value of $\mathrm{\frac{P Q^{2}}{P Z^{2}}+\frac{P Y^{2}}{P X^{2}}-\frac{P Z^{2}}{P Q^{2}}}$ is equal to
Option: 1
0

Option: 2
1

Option: 3
2

Option: 4
3

Answers (1)

best_answer

$\mathrm{PX}=\mathrm{PY}, \mathrm{PA} . \mathrm{PY}=\mathrm{PZ} . \mathrm{PB}$
$\mathrm{PX.PA =P Q \times P B}$

$\mathrm{\therefore \mathrm{PZ}=\mathrm{PQ}}$
$\mathrm{\therefore \frac{P Z}{P Q}=\frac{P X}{P Y}=1}$

Posted by

Ajit Kumar Dubey

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