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  4. Circle ' C prime has a diameter PQ and PS perpendicular to each other P X is any chord intersecting RS at Y, then PY. P X is equal to which one of the following?

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Q. Circle ' $C ^{\prime}$ has a diameter $PQ$ and $PS$ perpendicular to each other $P X$ is any chord intersecting $RS$ at $Y$, then $PY$. $P X$ is equal to which one of the following?

Geometry

Solution:

image
Join XQ.
Since angle PXQ is inscribed on diameter
So, $\angle PXQ =90^{\circ}$
By Angle Angle similarity
$\triangle PYC$ and $\triangle PQX$ are similar
So $\frac{P Y}{P C}=\frac{P Q}{P X}$
$P Y \cdot P X=P Q \cdot P C$