construction of tangents from a outside point when centre is unknown

dear student,

perhaps what you mean is how to construct a tangent  when the centre is unknown.

draw any two chords of the circle.Construct their  their perpendicular bisectors.Point of intersection of the perpendicular bisectors is the centre since it is equidistant from the end points of the chord and the end points of a chord obviously are the points on the circumference.

so we have found a point that is equidistant from at least three non collinear points , so it is the centre of the circle passing thru those points.

rest of the procedure for construction  of the tangen is same when the centre is given.