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largest ball in pyramid given side equations

Source: Bulgaria 1987 P3

June 15, 2021
geometry3D geometrypyramid

Problem Statement

Let MABCDMABCD be a pyramid with the square ABCDABCD as the base, in which MA=MDMA=MD, MA2+AB2=MB2MA^2+AB^2=MB^2 and the area of △ADM\triangle ADM is equal to 11. Determine the radius of the largest ball that is contained in the given pyramid.
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