circle_tangency

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

No annotations are provided, so the description carries the full burden of behavioral disclosure. It only states what the tool does ('Check tangency relationship') without describing any behavioral traits—such as whether it's a read-only operation, what the output format might be, error conditions, or computational constraints. This is inadequate for a tool with parameters and no annotations.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is extremely concise—a single sentence that directly states the tool's purpose and includes domain/category context. There is no wasted verbiage, and it is front-loaded with the core functionality. This efficiency is appropriate for a mathematical tool.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Given the tool's complexity (4 parameters, no annotations, no output schema), the description is incomplete. It lacks essential details: parameter meanings, behavioral traits, output expectations, and usage guidelines. While conciseness is good, the description does not provide enough context for an agent to use the tool effectively without additional external knowledge.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

The schema description coverage is 0%, and the description provides no information about the four integer parameters (p1, q1, p2, q2). It does not explain what these parameters represent (e.g., numerators and denominators of fractions defining Ford circles) or their constraints. With zero coverage and no compensatory details, the description fails to add value beyond the bare schema.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Does the description clearly state what the tool does and how it differs from similar tools?

The description clearly states the tool's purpose: 'Check tangency relationship between two Ford circles.' It specifies the verb ('Check'), resource ('tangency relationship'), and domain context ('Ford circles', 'arithmetic', 'farey_sequences'). However, it does not explicitly differentiate from sibling tools like 'ford_circle_properties' or 'ford_circles', which prevents a perfect score.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category but offers no explicit when/when-not instructions or references to sibling tools. This leaves the agent without practical usage context.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.