Hypothesis: AB is the diameter, the line a passes through A and is tangent to the semicircle, the line b passes through B and is tangent to the semicircle, the line EF passes through P and is tangent to the semicircle. P is any point of the semicircle and E and F are the intersections of the line passing through P and tangent to the semicircle with line a and b.

Thesis: PE * PF = (1/4) * AB^2 .

I hope I explained well the problem, otherwise I'll write it again! Thank you!