Question

Take a circle with centre $C$ and construct a tangent to a circle from an external point $P$.

Answer 1

Consider a circle with centre $C$ and a point $P$ lies outside the circle. Draw line $CP$ and find perpendicular bisector and mark the mid point.

At mid point $M$

Draw a circle of of radius $CM=MP$.

This circle intersect the given circle at two point $A$ and $B$. These are required tangent.