Fixed-point photography with equal sides of triangular pyramid

Let point p be plane ABC and projection o,

Connect OA, OB, OC,

Three sides of a triangular pyramid are equal,

∴PA=PB=PC，

∵PO⊥ bottom ABC,

PO⊥OA,PO⊥OB,PO⊥OC，

∴△PAO≌△POB≌△POC

∴OA=OB=OC

So o is the outer center of the triangle.

So choose C.