Find the midpoint of chord
This is a simple drawing for discussion about some properties of chords.
Imagine a very big circle (such as a construction site) where you can only access part of it. You have to locate the midpoint of the chord CD and join it with the centre A. There are obstacles near C and D, so you can't measure CD.
This scenario opens up a discussion about alternative means to locate the midpoint and shift their attention to angle (which is more readily accessible in this situation).
You may drag E and ask students to estimate when it will be the midpoint.
You may start with the centre A visible for the initial estimation.
Afterwards, you may use 
to drag the whole picture aside so that A (or even C) is no longer visible. Ask the students to estimate again and state clearly what exactly they can rely on.
to drag the whole picture aside so that A (or even C) is no longer visible. Ask the students to estimate again and state clearly what exactly they can rely on. 