### Some(?) of the Parts

A circle touches the lines OA, OB and AB where OA and OB are perpendicular. Show that the diameter of the circle is equal to the perimeter of the triangle

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

### At a Glance

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?

# Where Is the Dot?

##### Stage: 4 Challenge Level:

Watch the film below.

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This text is usually replaced by the Flash movie.

Imagine the dot starts at the point $(1,0)$ and turns anticlockwise.

Estimate the height of the dot above the horizontal axis after it has turned through $45^\circ$.

Estimate the angle that the dot needs to turn in order to be exactly $0.5$ units above the horizontal axis.

Show how you can use Pythagoras' Theorem to calculate the height of the dot above the horizontal axis after it has turned through $45^\circ$.

Again, without resorting to Trigonometry, calculate the height of the dot above the horizontal axis after it has turned through $30^\circ$ and $60^\circ$?

Are there any other angles for which you can calculate the height of the dot above the horizontal axis?