If 1,ω,ω² are the cube roots of unity, then (1-ω+ ω²)5+(1+ω- ω²)⁵ is equal to

The length of the tangent from a point on the circle x²+y²+4x-6y-12=0 to the circle x²+y²+4x-6y+4=0 is

The foot of the perpendicular from (0, 2, 3) to the line (x+3)/5 = (y-1)/2 = (z+4)/3 is:

A: The angle between the tangents drawn from origin to the circle x²+y²-14x+2y+25=0 is π/2

R: If θ is the angle between the pair of tangents drawn from (x₁, y₁) to the circle S=0 of radius r then tanθ/2=r/√S₁₁

A: The equation of the common chord of the two circles x²+y²+2x+3y+1=0, x²+y²+4x+3y+2=0 is 2x+1=0

R: If two circles intersect at two points then their common chord is the radical axis

The equation of the circle which bisects the circumference of the circle x²+y²=1,  x²+y²+2x=3, x²+y²+2y=3 is

The equation of the circles whose radius is 3 and which touches the circle x²+y²+2x+6y-15=0 externally at the point (2, 1) is

cos(α+β+γ)+cos(α-β-γ)+cos(β-γ-α)+cos(γ-α-β) is equal to:

The equation of the circle passing through the point (1, 2) cutting the circle x²+y²-2x+8y+7=0 orthogonally and bisects the circumference of the circle x²+y²=9 is

Origin is the centre of a circle passing through the vertices of an equilateral triangle whose median is of length 3a, then the equation of the circle is