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On Time

On a clock the three hands - the second, minute and hour hands - are on the same axis. How often in a 24 hour day will the second hand be parallel to either of the two other hands?

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Right Time

At the time of writing the hour and minute hands of my clock are at right angles. How long will it be before they are at right angles again?

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Estimating Angles

How good are you at estimating angles?

Subtended Angles

Age 11 to 14 Challenge Level:

If you are having difficulty with the interactivity, you may find this helpful:

* To create a rubber band for placing on your peg board, click on the colour of band that you would like to use, in the right-hand-side table.

* A new icon will appear on the screen. Drag this rubber band over to a peg on the board. Let go.

* You can now drag the rubber band to different pegs. To create another rubber band, repeat the above.


Join all the points up to the centre and look for isosceles triangles.

You may find this diagram helpful to get you started.



It is useful to note that the blue lines are all radii of the circle, and as such, are all the same length. You may want to use some algebra to help explain your proof .