CBSE Class 10 Answered

For Direct common Tangent:

Draw a radius of one circle [e.g. up to the right.]
Draw one in the second, parallel to the first.  Extend the line joining points
of intersection of radii with the circles to meet the [horizontal] line joining
their centers at P.
Use that point with one of the far left points of an original circle diameter on
the horizontal line to draw a semi-circle [full for both tangents.]  It will
intersect the first circle at the required point of tangency.  Join the far
point, P, to that for the common tangent.

For Transverse common tangent: