AI 기하학 문제 풀이기

The AI Geometry Problem Solver is different from the algorithm-driven calculators elsewhere on this site. Instead of fixed input fields and a pre-coded formula, you describe your problem in plain English (or upload a photo of it), and a large language model — currently a routing mix of Claude, GPT, and DeepSeek-VL — works through the problem step-by-step and returns a complete textbook-style solution. This tutorial covers when to use this tool versus a specialized calculator, how to phrase a problem so the AI can solve it correctly, and what the AI can and cannot do.

When to use this tool

Reach for the AI Solver when:

• The problem is a word problem. "A ladder 12 feet long leans against a wall, with its base 5 feet from the wall. How high up the wall does it reach?" The AI parses the scenario, identifies the right-triangle setup, and applies the Pythagorean theorem with full explanation.
• You don't know which formula applies. The AI selects the appropriate approach (Law of Sines vs Cosines, similarity vs congruence, area decomposition, coordinate geometry) based on what you describe.
• You need a proof. "Prove that the diagonals of a parallelogram bisect each other." A specialized calculator gives a number; only the AI can write the two-column or paragraph proof.
• You uploaded a photo of a problem from a textbook or whiteboard. Click the photo icon — the AI reads the image, transcribes the problem, and solves it.
• You want to check your own work. Describe the problem and your answer; the AI will tell you whether it agrees and where it diverges.

When to use a specialized calculator instead

For purely numerical problems with a known formula, the specialized calculators are faster, cheaper, and more reliable:

• Need triangle area from three sides? Use the Triangle Solver or Heron's Formula Calculator.
• Need circle area or circumference from radius? Use the Circle Geometry Calculator.
• Need to find a missing side via Pythagorean theorem? Use the Pythagorean Theorem Calculator.
• Need volume of a sphere/cylinder/cone? Use the Sphere/Cylinder/Cone Calculator.

The specialized calculators give exact answers in milliseconds and don't consume AI credits. The AI Solver shines on problems where the formula isn't obvious or where the explanation matters as much as the answer.

How to write a problem the AI can solve

The AI does best when the problem includes:

1. The geometric setup. What shape(s) are involved? How are they positioned relative to each other?
2. All known measurements. Give units. "5" is ambiguous; "5 cm" is clear.
3. What you want to find. "Find the area" or "Find angle B" — be explicit.
4. Any constraints. "Express the answer in terms of π" or "Round to 2 decimal places".

Good prompt: "A regular hexagon has a side length of 6 cm. Find its area, expressed in exact form (using √3 if needed) and as a decimal to 2 places."

Bad prompt: "Hexagon, area, 6." — the AI has to guess that you mean side length, that you want area, that it's regular, etc. It may guess right, but the answer will be less reliable.

What the AI is actually doing

Behind the scenes, your problem is sent to a large language model with a system prompt that instructs it to (1) restate the problem in mathematical notation, (2) identify the relevant formula or theorem, (3) carry out the calculation step-by-step, and (4) present the final answer with units and a brief verification.

The routing — which LLM gets your problem — depends on the type:

• General word problems and computation: OpenAI GPT (gpt-4o-class) for clarity of explanation.
• Proof-style problems: Anthropic Claude for rigorous step-by-step deductive reasoning.
• Photo / image problems: DeepSeek-VL or another vision-capable model that can read text and figures from the image.

You don't pick the model — the routing is set in the theme's AI handler (see our Methodology page).

What the AI cannot do reliably

• Hand-drawn figures without labels. The vision models can read printed text and standard textbook figures, but a quick sketch on a napkin without numerical labels may not be interpretable.
• Problems requiring software-only tools. If a problem specifically requires Mathematica, GeoGebra, or a CAS to solve, the AI may produce a step-by-step approach but the final symbolic answer may be incomplete.
• Open-ended research-level questions. "Conjecture and prove a new theorem about isogonal conjugates." The AI handles textbook-level material; novel theorem-proving is outside its reliable range.

Verifying the AI's answer

Always cross-check the final number with a specialized calculator when possible. The AI explanation may be perfect but the arithmetic in step 5 may have a typo. Our deterministic calculators ARE the verification step.

If you suspect an error, paste the problem into both this AI Solver AND a specialized calculator (or run the AI Solver twice and compare the answers). When two independent answer methods agree, the result is much more likely correct.

Credits and cost

AI Solve uses 3 credits per submission. New accounts receive 30 free credits (≈ 10 AI solutions). Premium plans include monthly credit allowances. Photo uploads also use 3 credits — the same as text input. See Pricing for details.

Common mistakes when prompting the AI

• Forgetting to specify units. "Find the area" assumes square units of whatever your side lengths used. If your problem is unit-agnostic, the AI will return unit-agnostic answers — which is usually fine, but be explicit if you need (say) square meters.
• Missing a constraint. If the answer "must be in exact form" or "must use a specific formula", say so. The AI may default to decimal approximations otherwise.
• Asking multi-step problems in one prompt. The AI handles them, but for very complex multi-part problems, splitting into 2-3 prompts gives clearer step-by-step explanations.