Step One: Construct a line. Then create a circle with center O.
Step Two: Construct a line that is perpendicular to the given line passing through the center O.
Step Three: Create lines that pass through points OP, AP, and BP.
Step Four: Draw two lines that are perpendicular to the given line at point C and point D. The point of intersection of lines l and n will be the center of one tangent circle, and the second tangent cirlce's center will serve as the intersecting point of lines n and m.
Step Five: Use the points of intersection created by each turquoise line with the line OP to construct two circles. These points will be the centers of the new circles, and the circles will be tangent to the given line and point P.
Like Animation. Be sure to click the button that says ANIMATE POINT. Notice that the two new circles are always tangent to the given line and point P.