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Students learning circle theorems for GCSE Mathematics often encounter these misconceptions:

- Misapplying theorems without recognising specific conditions required for each.
- Confusing the alternate segment theorem, applying it incorrectly due to misunderstanding conditions.
- Incorrectly assuming angle properties in circles without the necessary chords or tangents.
- Mixing up relationships between tangents and secants, leading to errors in angle size and segment length assumptions.
- Overlooking the importance of cyclic quadrilaterals and misinterpreting their angle relationships.

In this blog I share three examples that, in my experience, address these common misconceptions.

**Key Skills**: Understanding the intersecting chords theorem and the alternate segment theorem.

**Advice**: Highlight the significance of arc subtension and its relationship with the alternate segment’s angle. Use diagrams to visualize the concept.

**Check Questions**:

**Key Skills**: Applying the rule that the angle at the center is twice the angle at the circumference.

**Advice**: Employ varied examples showing central and circumferential angles from the same arc to consolidate the concept.

**Check Questions**:

- Having found angle e using circle theorems can you check this using a different property?
- Which circle theorem would you use to find angle e using the 80° angle.

**Key Skills**: Recognising that the angle between a tangent and radius is 90 degrees, and using algebraic notation to generalise an angle property.

**Advice**: Stress on identifying right angles and the relationship between tangent and radius. Demonstrate with tangents drawn at different points on the circle.

**Check Questions**:

- Identify and justify the right angles in the diagram.
- How can OXW and OWX be written algebraically?

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