Sketch a Line Tangent to two Circles:

To Sketch a Line Tangent to two Circles of Different Radius as like r and R:

Two cases are possible now uncrossed tangents as displayed via diagram (a) and crossed tangents as displayed via diagram (b). Uncrossed tangents are constructed in the given way. From O as the center and along with a radius equal to the difference of the radii of the given circle is like R - r, sketch an auxiliary circle. From the center O₁, sketch a line O₁ n, tangent to this circle at n. From the center O, sketch a radius, O_n, and extend it to intersect the circle R at m. Sketch the radius O₁K of the second circle parallel to the line Om. Connect the points K and m along with a straight line that will be tangent to the specified circles. Crossed tangents are constructed in a same way, except such the auxiliary circle is described along with a radius R + r. On drawing a line from O1 tangent to the auxiliary circle m, this point is joined along with O via radius Om, that intersects the circle OR at n. sketch a line parallel to o1m via n that gives line nK such is the desired cross-tangent.