The tangent and the normal lines at the point ( $$\sqrt 3 $$, 1) to the circle x² + y² = 4 and the x-axis form a triangle. The area of this triangle (in square units) is :

The sum of the squares of the lengths of the chords intercepted on the circle, x² + y² = 16, by the lines, x + y = n, n $$ \in $$ N, where N is the set of all natural numbers, is :

If a circle of radius R passes through the origin O and intersects the coordinates axes at A and B, then the locus of the foot of perpendicular from O on AB is :

Let C₁ and C₂ be the centres of the circles x² + y² – 2x – 2y – 2 = 0 and x² + y² – 6x – 6y + 14 = 0 respectively. If P and Q are the points of intersection of these circles, then the area (in sq. units) of the quadrilateral PC₁QC₂ is :