Transform ellipse back to circle

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I have a circle in a $xz$ plane with its center at Origin $O$ as shown in the diagram. The circle is being observed by a camera from point $C$ at $yz$ plane at an angle $\beta$ with the $z-$ Axis.

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From the cameras perspective, the circle appears like an ellipse and the actual radius $OP$ appears to be shorter and at an angle $P^{*}OQ$ with the $x-$ Axis. Is it possible to find the actual radius from this angle $P^{*}OQ$ and the length of reduced radius?

Thanks in advance!