120008 The common chord of the circles \(x^2+y^2-4 x-4 y=0\) and
\(2 x^2+2 y^2=32\) subtends at the origin an angle equal to

120009 The ratio of the areas of the concentric circles \(x^2+y^2-6 x+12 y+15=0\) and \(x^2+y^2-6 x+\) \(12 y-15=0\) is

120010 The two circles \(x^2+y^2=a x\) and \(x^2+y^2=c^2\), (c>
0 ) touch each other, if

120011 The number of common tangents to the circles \(x^2+y^2-4 x-6 y-12=0\) and \(x^2+y^2+6 x+18 y\) \(+26=0\) is

120012 Let \(\mathbf{C}_1\) and \(\mathbf{C}_2\) be the centres of the circles \(\mathbf{x}^2+\) \(y^2-2 x-2 y-2=0\) and \(x^2+y^2-6 x-6 y+14=\) 0 respectively. If \(P\) and \(Q\) are the points of intersection of these circles, then the area (in \(s q\) units) of the quadrillateral \(\mathrm{PC}_1 \mathrm{QC}_2\) is

120008 The common chord of the circles \(x^2+y^2-4 x-4 y=0\) and
\(2 x^2+2 y^2=32\) subtends at the origin an angle equal to

120009 The ratio of the areas of the concentric circles \(x^2+y^2-6 x+12 y+15=0\) and \(x^2+y^2-6 x+\) \(12 y-15=0\) is

120010 The two circles \(x^2+y^2=a x\) and \(x^2+y^2=c^2\), (c>
0 ) touch each other, if

120011 The number of common tangents to the circles \(x^2+y^2-4 x-6 y-12=0\) and \(x^2+y^2+6 x+18 y\) \(+26=0\) is

120012 Let \(\mathbf{C}_1\) and \(\mathbf{C}_2\) be the centres of the circles \(\mathbf{x}^2+\) \(y^2-2 x-2 y-2=0\) and \(x^2+y^2-6 x-6 y+14=\) 0 respectively. If \(P\) and \(Q\) are the points of intersection of these circles, then the area (in \(s q\) units) of the quadrillateral \(\mathrm{PC}_1 \mathrm{QC}_2\) is

120008 The common chord of the circles \(x^2+y^2-4 x-4 y=0\) and
\(2 x^2+2 y^2=32\) subtends at the origin an angle equal to

120009 The ratio of the areas of the concentric circles \(x^2+y^2-6 x+12 y+15=0\) and \(x^2+y^2-6 x+\) \(12 y-15=0\) is

120010 The two circles \(x^2+y^2=a x\) and \(x^2+y^2=c^2\), (c>
0 ) touch each other, if

120011 The number of common tangents to the circles \(x^2+y^2-4 x-6 y-12=0\) and \(x^2+y^2+6 x+18 y\) \(+26=0\) is

120012 Let \(\mathbf{C}_1\) and \(\mathbf{C}_2\) be the centres of the circles \(\mathbf{x}^2+\) \(y^2-2 x-2 y-2=0\) and \(x^2+y^2-6 x-6 y+14=\) 0 respectively. If \(P\) and \(Q\) are the points of intersection of these circles, then the area (in \(s q\) units) of the quadrillateral \(\mathrm{PC}_1 \mathrm{QC}_2\) is

120008 The common chord of the circles \(x^2+y^2-4 x-4 y=0\) and
\(2 x^2+2 y^2=32\) subtends at the origin an angle equal to

120009 The ratio of the areas of the concentric circles \(x^2+y^2-6 x+12 y+15=0\) and \(x^2+y^2-6 x+\) \(12 y-15=0\) is

120010 The two circles \(x^2+y^2=a x\) and \(x^2+y^2=c^2\), (c>
0 ) touch each other, if

120011 The number of common tangents to the circles \(x^2+y^2-4 x-6 y-12=0\) and \(x^2+y^2+6 x+18 y\) \(+26=0\) is

120012 Let \(\mathbf{C}_1\) and \(\mathbf{C}_2\) be the centres of the circles \(\mathbf{x}^2+\) \(y^2-2 x-2 y-2=0\) and \(x^2+y^2-6 x-6 y+14=\) 0 respectively. If \(P\) and \(Q\) are the points of intersection of these circles, then the area (in \(s q\) units) of the quadrillateral \(\mathrm{PC}_1 \mathrm{QC}_2\) is

120008 The common chord of the circles \(x^2+y^2-4 x-4 y=0\) and
\(2 x^2+2 y^2=32\) subtends at the origin an angle equal to

120009 The ratio of the areas of the concentric circles \(x^2+y^2-6 x+12 y+15=0\) and \(x^2+y^2-6 x+\) \(12 y-15=0\) is

120010 The two circles \(x^2+y^2=a x\) and \(x^2+y^2=c^2\), (c>
0 ) touch each other, if

120011 The number of common tangents to the circles \(x^2+y^2-4 x-6 y-12=0\) and \(x^2+y^2+6 x+18 y\) \(+26=0\) is

120012 Let \(\mathbf{C}_1\) and \(\mathbf{C}_2\) be the centres of the circles \(\mathbf{x}^2+\) \(y^2-2 x-2 y-2=0\) and \(x^2+y^2-6 x-6 y+14=\) 0 respectively. If \(P\) and \(Q\) are the points of intersection of these circles, then the area (in \(s q\) units) of the quadrillateral \(\mathrm{PC}_1 \mathrm{QC}_2\) is