How to prove this tangent to a circle?

Question

the circles c1 and c2 have equations
x^2 + y^2 = 20 and x^2 + y^2 - 24x -12y +100 = 0 respectively 

the centre and radius of c1 is (0,0) and square root of 20 
the centre and radius of c2 is (12,6) and square root of 80 

prove that the tangent to the two circles has equation y+2x = 10 

how do you do this ?
thanks

Answer 1

x² + y² = 20-------------->(1).

x2 + y2 - 24x - 12y + 100 = 0---------->(2)

Substitute the equation(1) in the equation(2).

20 - 24x - 12y + 100 = 0

-24x - 12y + 120 = 0

Divide each side by -12.

2x + y - 10 = 0

Subtract 10 from each side.

2x + y = 10.

Therefore the tangent to the circles has equation is 2x + y = 10.