2022 SSMO Speed Round Problems/Problem 4: Difference between revisions
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==Problem== | |||
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== | |||
Revision as of 18:14, 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 
.
