Through point A are drawn tangents AB (B is the point of tangency) and a secant that intersects the circle at points P

Through point A are drawn tangents AB (B is the point of tangency) and a secant that intersects the circle at points P and Q. Prove that AB in q = AP * AQ. for this I know it is necessary to prove that triangle ABP is similar to triangle AQB, but how to prove that angle Q = angle ABP

Let’s connect points B and Q.

Let us prove the similarity of triangles ABP and ABQ.

Angle A is common for triangles. The angle ABH between the chord and the tangent is equal to half of the arc PB, and the inscribed angle BQP is also equal to half of the arc PB on which it rests, then the angle ABP = BQP, and the triangles ABP and ABQ are similar in two angles.

Then in similar triangles: AB / AQ = AP / AB.

AB ^ 2 = AP * AQ, as required.