Food for thought

# A limiting circle theorem Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

## Problem

In this interactivity, you can move the points $A$, $B$, $C$ and $D$ around the circumference of the circle, with $D$ between $B$ and $C$.

1. Three angles are marked.

What can you say about the angles at $C$ and $D$?

What happens to these angles if you move $C$ or $D$, keeping $A$ and $B$ fixed?

How do you know this?

2. What happens to the exterior angle at $B$ (shown in blue) as $D$ approaches $B$?

3. Which other circle theorem can you deduce from this?