For tangent problems, always first check whether to use the point form (T=0) or slope form (y=mx+/-asqrt(1+$m^2$)). Use point form when the point of tangency is known or sought; use slope form when the tangent's slope is given. For two-circle problems, start by computing d, r1, r2 to determine the configuration. Use the radical axis S1-S2=0 for common chord problems. For family of circles through intersection, use S1+lambdaS2=0 with the additional condition to determine lambda. For orthogonality, apply 2g1g2+2f1f2=c1+c2. For tangent length and power problems, compute S1 directly. When asked for the equation of a circle satisfying three conditions (passing through points, tangent to lines, orthogonal to circles), set up three equations in g, f, c. The T=0 technique is the most versatile tool — master it thoroughly and recognize when chord of contact, chord with midpoint, or pair of tangents is being asked.