Today is rung 5 of 6 on this topic
Circle theorems and arc relationships
Can do: Applies the circle theorems and explains which one justifies each step.
Why it matters
Circles carry more theorems than any other topic, and the difficulty is recognising which configuration you're looking at.
What it looks like when it's wobbly
Knows the theorems in isolation but cannot spot which applies in a cluttered diagram.
⏱️ Two-minute check
Give a circle diagram with a central and an inscribed angle on the same arc. "Find the missing angle and name the theorem."
Solid looks like: Correct value and the theorem named.
The full activity for this topic · 30 minutes
One Diagram, All the Theorems
- 1Draw one large circle and add a chord, a tangent, a central angle and an inscribed angle.
- 2Measure everything and look for the relationships before being told them.
- 3Write each theorem next to the part of the diagram that shows it.
- 4Then solve problems, naming the theorem for every step.
- 5Make a one-page reference sheet with a small diagram for each theorem.
If it's too hard
One theorem at a time with clean diagrams.
If it's too easy
Multi-step problems needing three theorems, plus a proof of one of them.
Say this
"Which configuration is that? Find the shape you recognise inside the mess of lines."