C
CraftExam
medium difficulty5 min

Constructing argument from circle diagram

This means building a correct geometric conclusion from the marks and labels in a circle figure.

In one line: Mark it, match it, prove it.

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Understand it

  • A good circle answer starts with observation.
  • You identify tangents, radii, equal lengths, and right angles from the diagram, then connect them using the correct theorem.
  • Many students know the facts but do not know how to organise them into a proper argument.
  • This concept trains that skill.

Example

From a diagram, if OA and OB are radii to tangent points A and B, you can argue OA ⟂ tangent at A and OB ⟂ tangent at B.

Formula and rule

Use the given diagram marks as evidence for tangent and radius properties, then build the proof logically.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

If a diagram shows OA and OB as radii to two tangent points, then the perpendicular property helps you establish right angles, which can then support triangle congruence.

Method you can reuse

  1. 1List the given parts in the diagram.
  2. 2Name the tangent and radius pairs.
  3. 3Apply the correct theorems.
  4. 4Write the conclusion using clear reasons.

Sketch it in your answer

Label every known point and every given equal mark before starting the proof sentences.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

What should you do first when asked to prove a result from a circle diagram?

Think first, then show answer
First identify the given marks, such as radii, tangents, equal lengths, and right angles. Then connect them with the correct theorem before writing the final conclusion.

Common wrong answer

A common wrong answer is to describe the picture without proving anything. A geometry answer needs reasons, not only observations.

Don't mix this up

Students often write conclusions before giving the reason chain from the diagram.

Exam tip

Read the diagram like a proof: mark, identify, then conclude.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

This is common in proof-based questions where the figure is given and students must justify a statement step by step.
  1. 1

    Enough for 1 mark

    This means building a correct geometric conclusion from the marks and labels in a circle figure.

  2. 2

    Add for 2 marks

    A good circle answer starts with observation.

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