Difference between revisions of "2022 SSMO Speed Round Problems/Problem 4"
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==Problem== | ==Problem== | ||
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+ | Consider a quadrilateral <math>ABCD</math> with area <math>120</math> and satisfying <math>AB+CD=AD+BC=24</math>. There exists a point <math>P</math> in 3D space such that the distances from <math>P</math> to <math>AB</math>, <math>BC</math>, <math>CD</math>, and <math>DA</math> are all equal to <math>13</math>. Find the volume of <math>PABCD</math>. | ||
==Solution== | ==Solution== | ||
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Latest revision as of 19:14, 2 May 2025
Problem
Consider a quadrilateral with area
and satisfying
. There exists a point
in 3D space such that the distances from
to
,
,
, and
are all equal to
. Find the volume of
.