P and Q are the ends of a diameter of the circle {\x}^2+ {\y}^2= {\a}^2 ( {\a}> {1}/{\sqrt{2}}) \cdot s and t are the lengths of the perpendiculars drawn from P and Q onto the line {\x}+ {\y}=1 respectively. When the product s t is maximum, the greater value among s, t is [AP EAPCET 23 May 2025 S1]