Constructing a tangent to a circle at a point on the circle
Let A be the point on the circle through which a tangent shall be drawn. We select any four points on the circle B, C, D, E
We construct the chords AC, AD, BD, BE and CE.
We denote by K the point of intersection of the chords AC and BD.
We denote by L the point of intersection of the chords AD and EC.
We connect the points K and L by a straight line. The continuation of the straight line LK intersects the continuation of the chord BE at the point P. The straight line connecting the points P and A is the sought tangent AP.