Ab patented formula in milk powder

The topic condition should be that the circle O with diameter AC intersects BC at point P, and Q is the midpoint of AB.

Because if BC is the diameter, then △ABC will be inscribed on the circle O (△ABC is the right triangle and BC is the hypotenuse).

Proof: As shown in Figure AB, it is the tangent of circle O.

∴∠3=∠BCA

∠∠BCA+∠ABC = 90

∴∠3+∠ABC=90

∴AP⊥BC？ Q is the midpoint of AB.

∴AQ=QP

∴∠3=∠4

AO = PO

∴∠ 1=∠2? Similarly < 3+<1= 90

∴∠2+∠4=∠ 1+∠3=90

∴QP⊥PO

∴PQ is the tangent of circle O.