Here are several challenging geometry prompts based on the difficulty level you mentioned (6-8):

1. Find the locus of points P such that the area of triangle ABC, where A, B, and C are fixed points, remains constant as P moves.

2. Given a regular hexagon inscribed in a circle, find the locus of points such that the sum of the distances from these points to two non-adjacent vertices of the hexagon is constant.

3. Prove that for any convex quadrilateral inscribed in a circle, the sum of the squares of the lengths of the diagonals is constant, regardless of the shape of the quadrilateral.

4. Find the equation of the locus of points that are equidistant from two intersecting circles.

5. Determine the largest possible area of a triangle that can be inscribed in a circle of radius 1, given that one side of the triangle is parallel to a fixed line.

Would you like me to elaborate on any of these or create more specific ones? Also, feel free to ask if you'd like further clarification on any particular geometry concept!

Here are some related questions you could explore further:

1. How do the properties of loci relate to geometric transformations like translations and rotations?
2. What is the geometric significance of constant sums or areas in relation to inscribed polygons?
3. How does one approach solving geometric problems involving multiple fixed points and moving loci?
4. Can you find similar results in other conic sections such as ellipses or hyperbolas?
5. How do concepts like symmetry and center of mass play a role in these types of geometric problems?

Tip: When dealing with loci problems, it can be helpful to start by using coordinate geometry and algebraic representations of shapes to simplify the problem-solving process.