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Truncated Trigonal [s]Pyramid[/s] Trouble!

Source: XVII Sharygin Correspondence Round, P24

March 2, 2021
geometry3D geometrypyramid

Problem Statement

A truncated trigonal pyramid is circumscribed around a sphere touching its bases at points T1,T2T_1, T_2. Let hh be the altitude of the pyramid, R1,R2R_1, R_2 be the circumradii of its bases, and O1,O2O_1, O_2 be the circumcenters of the bases. Prove that R1R2h2=(R12−O1T12)(R22−O2T22).R_1R_2h^2 = (R_1^2-O_1T_1^2)(R_2^2-O_2T_2^2).
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