Prove that the circle `x^2 + y^2 =a^2 and (x-2a)^2 + y^2 = a^2` are equal and touch each other. Also find the equation of a circle (or circles) of equal radius touching both the circles.

Prove that x^2+y^2=a^2 and (x-2a)^2+y^2=a^2 are two equal circles touching each other.

Prove that x^2+y^2=a^2 and (x-2a)^2+y^2=a^2 are two equal circles touching each other.

Show that the circles x^2 + y^2 + 2x-8y+8=0 and x^2 + y^2 + 10x - 2y+ 22=0 touch each other. Also obtain the equations of the two circles, each of radius 1, cutting both these circles orthogonally.

The equation of a circle of radius 1 touching the circle x^2 + y^2 - 2|x| = 0 is

Find the equation of a circle with center (4, 3) touching the circle x^2+y^2=1

Find the equation of a circle with center (4,3) touching the circle x^(2)+y^(2)=1

Find the equation of a circle with center (4, 3) touching the circle x^2+y^2=1

Prove that the circle x^(2)+y^(2)+2x+2y+1=0 and circle x^(2)+y^(2)-4x-6y-3=0 touch each other.

Prove that the circle x^(2)+y^(2)+2x+2y+1=0 and circle x^(2)+y^(2)-4x-6y-3=0 touch each other.