$\underline{\text { Gordrin P.K. }}$.

Between two parallel lines, a circle of radius 1 is placed, touching both lines, and an isosceles triangle, the base of which lies on one of the lines, and the vertex on the other. It is known that the triangle and the circle have exactly one common point and that this point lies on the inscribed circle of the triangle. Find the radius of the inscribed circle of the triangle.