Construct a tangent line from an external point to a circle.
Audit an external-tangent construction
Problem
A proposed tangent construction correctly finds midpoint \(M\) of \(OP\) but draws the auxiliary circle with radius \(OP\). Identify the first invalid step, give the correct radius in terms of \(MO\), \(MP\), and \(OP\), and state why the correction makes \(OP\) a diameter.
