2022 SSMO Speed Round Problems/Problem 4

Problem

Consider a quadrilateral $ABCD$ with area $120$ and satisfying $AB+CD=AD+BC=24$ . There exists a point $P$ in 3D space such that the distances from $P$ to $AB$ , $BC$ , $CD$ , and $DA$ are all equal to $13$ . Find the volume of $PABCD$ .

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2022 SSMO Speed Round Problems/Problem 4

Problem

Solution