two circlea with radius 5 touches at the point (1,2). If the equation of common tangent is 4x+3y=10 and one of the circle is x^2+y^2+6x+2y-15=0. Find the equation of other circle

If u draw the diagram then u will relaise that the circlea are orthogonal means they aee touching externally. And point (1,2) will lie on the common cbord of the circle and also the radius are equal . So therefore (1,2)is the mid point of both the circles so by that centre of another circle is (-1,5) therefore the equation of circle is x^2 + y^2 + 2x -10y +1 = 0.