<Solid-2025-263>, hint

Let O be the center of sphere ABCD, vectors OA=a, OB=b, OC=c, OD=d

ADㅗBC ; (a-d)(b-c)=0, ACㅗBD; (a-c)(b-d)=0, thus  ac+bd=ad+bc (a-b)(c-d)=0

ABㅗCD . A regular tetrahedron satisfies above condition