After departing Miami and climbing through 10,900 ft, the #3 right main landing gear tire exploded causing massive damage to systems A & B hydraulic lines which resulted in a loss of A & B hydraulic systems. The aircraft returned to Miami and the crew was unable to extend the right main landing gear using emergency manual extension procedures. After landing with the right main gear retracted, the left main and nose gear collapsed and separated. Massive ply separations were found in the #3 tire starting at the toe bead, down the sidewall, and extending circumferentially around the crown of the tire at the 10th to 13th ply layers. Inspection of the site where the separation met the bead bundles revealed a location where the bead seat had been sanded and smoothed. The abrasion had removed the outer chafer strip, several cover plies, and had exposed the plies covering the toe bead. The bead seat, as well as the cords wrapped around the toe bead, had also been subjected to excessive heat for an extended period of time causing severe deterioration of the bead seat area.