How to prove the five points of ABCD on the same sphere: B, C and D

According to the meaning of the question, △ABC is an equilateral triangle with an area of 334, and the radius of the circumscribed circle is 1. The center of the small circle is Q. If the volume of the tetrahedron ABCD is the largest, then the bottom area S△ABC is constant, and the volume is also the largest when the height is the largest, so the volume is the largest when ∴DQ=4 is perpendicular to the surface ABC, and the maximum value is 13s △ ABC. Then in the right angle △AQO, OA2=AQ2+OQ2, that is, R2= 12+(4-R)2 and ∴R= 178, the surface area of this ball is: S = 4π (178) 2 = 288.