(Originais Teachy 2024) - Question Medium of Mathematics

In an amusement park, there is a Ferris wheel located at a point with known coordinates representing the center of the circumference traveled by its cabins. Two lights, one at each horizontal end of the wheel's diameter, project onto the ground forming a 60-degree angle with the line connecting the center of the wheel to the projection points. A visitor observes that the intersection point of these lights is at a distance of 10 meters from the center of the Ferris wheel. (a) Considering that the center of the Ferris wheel is the point (h, k) and the radius is R, determine the equation of the circumference that describes the movement of the Ferris wheel cabins. (b) Evaluate and discuss the visitor's position in relation to the equation and the radius of the Ferris wheel, providing a mathematical justification for your conclusion.