The Necessity of the Incarnation

I'm teaching on the Incarnation & the Hypostatic Union this Friday, and as I've been thinking about the subject, a few questions from the Heidelberg Catechism came to mind:

15. What kind of a mediator and redeemer then must we seek?
One who is a true and righteous man, and yet more powerful than all creatures, that is, One who is also true God.

16. Why must he be a true and righteous man?
Because the justice of God requires that the same human nature which has sinned should make satisfaction for sin, but one who is himself a sinner, cannot satisfy for others.

17. Why must he also be true God?
That by the power of His Godhead He might bear in His manhood the burden of God's wrath, and so obtain for and restore to us righteousness and life.

18. But who now is that Mediator, who in one person is true God and also a true and righteous man?
Our Lord Jesus Christ, who is freely given unto us for complete redemption and righteousness.