The mystery of Christ means that two natures, undiminished by each other, became one in a single Person. Because there is a division of natures in Christ, there is also a division of intellects: the Human and the Divine. From the very beginning of the Incarnation, the Word was endowed with a perfect knowledge of God, or the beatific vision; but there is still a mysterious interplay of the two intellects of the God-Man, because Christ, as a man, was subject to experimental knowledge like the rest of us, as He assumed human nature in all things, save sin.
Truly, Christ is the very Word of God, and because of this fact He is consubstantial with the Father and the Holy Spirit, in power, presence, perfection and knowledge. When the Word of God became flesh, He assumed an inheritance of experimental knowledge, to share in our human state. This does not end up detracting from the wholeness of the Divine; Christ’s Humanity is beside and in cooperation with his Deity.
How is this possible? I don’t know. Consult the theologians of the Church, from all ages. They’ve fought many heretical groups over Christology, including the Arians, the Monophysites etc., many of which share the same qualms about these involved doctrines as do our Muslim brothers and sisters.