Conventionally, the secant angle equals half the sum ...

The equality isn't conventional, it is actual. I think the sentence would be more correct without the opening adverb. There may be another adverb that would be OK here.

The next sentence, the first comma (after case) doesn';t really belong there.

Just below the figure,

This creates a triangle ACD with and external angle BDC.

should be

This creates a triangle ACD with an external angle BDC,"

>The equality isn't conventional, it is actual.

You are right.

>The next sentence, the first comma (after case) doesn';t
>really belong there.

Usually a tangent is not called a secant. Thus I believe what was said previously does not automatically extend to the case of a tangent and a secant. Thought it is reasonable to give the case a special mention.

>should be
>This creates a triangle ACD with an external angle BDC,"

Yes. Thank you again.

Alex