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