This question is not very difficult, but it involves a lot of knowledge. It examines the properties of circles, the tangency of two circles, and the relationship between setting side lengths to represent other side lengths, and then solving them with right triangles. The overall problem is not difficult, and it is worth practicing. The answer/exercise/math /799260 is the senior high school entrance examination this year. I wish you better study. Come on, I hope you will adopt it. You won't ask me again.

In Rt△ABC, ∠ ACB = 90, AC=4cm, BC=3cm, and ⊙O is the inscribed circle of △ABC.

(1) Find the radius of ⊙O;

(2) Point P moves from point B to point A along the edge of BA at a constant speed of 1cm/s to make a circle with P as the center and PB as the radius. Let point P move as t s, and if ⊙P is tangent to ⊙O, find the value of T. 。

Considering that two circles are tangent and one circle is fixed, there are generally two situations, circumscribed and inscribed. Therefore, it should be discussed separately. When circumscribed, the center distance is equal to the sum of the radii of two circles; When inscribed, the center distance is equal to the difference between the radius of the big circle and the radius of the small circle. Construct right triangles with vertical lines respectively, which is similar to the value easily obtained by expressing the relationship between side lengths.