A problem of solid geometry

the perpendicular of plane ABC crossing point P crosses plane ABC at O, connecting AO and extending BC at D, connecting PD,BC perpendicular to PA, and PO perpendicular to PA, so PA is perpendicular to plane PAD,AD perpendicular to BC, connecting BO and extending AC at E. Similarly, it can BE proved that Be is perpendicular to AC, connecting CO and extending AB at F. Since AD is perpendicular to BC and Be is perpendicular to AC, point O is the vertical center of triangle ABC.