Proof of law of reflection

Question

When proving the law of reflection using huygens construction I do not understand why a tangent is drawn to the semi-circle (i.e the line CD)

Answer 1

The tangent makes sense only as a common tangent to semicircles of different radii centred on different points on AC and representing 'wavelets' emitted from different points on the reflector when the incident wavefront AB hits them. The common tangent is the 'envelope' of the secondary waves and, according to Huygens's principle is the reflected wavefront.

If I may say so, your diagram isn't very helpful, and it's irritating that the directions of propagation aren't at right angles to the wavefronts!