The problem is from Kiselev's Geometry Exercise 582:
A circle of the radius congruent to the altitude of a given isosceles triangle is rolling along the base. Show that the arc length cut out on the circle by the lateral sides of the triangle remains constant.
[Edited] The problem is very vague, but the correct version of it is that the circle should either pass through the top vertex or both lateral sides.
My attempt was to draw a line parallel to the base and passing through the top vertex. Then the case when the circle passes through the top vertex is easy since the side angle formed by the intersection of the circle and a lateral side is the same as the side angle of the given isosceles triangle. However, I could not derive the same conclusion when the circle intersects both lateral sides.
Any help would be greatly appreciated.