Let the tangents drawn to the circle x² + y² = 16 from the point P(0, h) meet the x-axis at points A and B. If the area of ΔAPB is minimum, then h is equal to:

Given circle is x² + y² = 16 and tangents are drawn from P(0, h) such that they intersect x-axis at A and B. Area of ΔAPB is minimum, only when it is a right-angled triangle with right angle at P.
∴ Equations of AP and BP are x + y - h = 0 and x - y + h = 0 respectively. As AP is tangent to the circle, distance from origin to x + y - h = 0 is equal to radius.
⇒ h/√2 = 4
∴ h = 4√2
Hence, option D.