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task_geometry__circle_centerline_overlap__segment_length_value

Contract

  1. Domain: geometry
  2. Scene id: circle_centerline_overlap
  3. Query id: center_distance_from_overlap or boundary_segment_from_overlap
  4. Answer schema: integer_value
  5. Annotation schema: segment

Program Contract

  • solve_formula(visible_collinear_circle_overlap_measurements, unknown_role=target_centerline_segment, formula_schema=circle_centerline_overlap_segment_length); scene=circle_centerline_overlap; scope=segment_length_value

Reasoning Operations

Families: formula_evaluation

Prompt Bundle

  • Prompt text is loaded from geometry_circle_centerline_overlap_v1.
  • Prompt modes: answer_only and answer_and_annotation.

Annotation

Prompt-facing annotation uses one pixel-space segment for the requested target segment only: [[x0,y0],[x1,y1]]. For example, if the prompt asks for AB or AC, the segment endpoints are the visible center points. If it asks for a boundary segment such as AP or QB, the endpoints are the visible center/boundary points named in the target segment. Numeric labels, point labels, radius readouts, and known segments remain visible context plus private verifier metadata.

Sampling

Default generation samples two-circle chains 75% of the time and three-circle chains 25% of the time as internal construction metadata. It samples circle radii and adjacent overlap lengths from deterministic constrained integer ranges instead of a small fixed case bank. The constraints preserve proper adjacent circle overlaps, keep non-adjacent circles separated for three-circle chains, and ensure boundary-segment answers remain at least 3. Boundary labels are left-to-right along the centerline: P,Q for the first overlap and R,S for the second overlap when present. Circle measurement labels are radius labels.

Determinism

Generation is deterministic for a fixed seed, params, config, and prompt bundle version.

Source

  • Config: src/trace_tasks/resources/configs/domains/geometry/circle_centerline_overlap.yaml
  • Task module: src/trace_tasks/tasks/geometry/circle_centerline_overlap/segment_length_value.py