What is the same and what is different about these circle questions? What connections can you make?

The diagonals of a square meet at O. The bisector of angle OAB meets BO and BC at N and P respectively. The length of NO is 24. How long is PC?

You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?

Can you make sense of these three proofs of Pythagoras' Theorem?

The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?

Can you make sense of the three methods to work out the area of the kite in the square?

In the diagram the radius length is 10 units, OP is 8 units and OQ is 6 units. If the distance PQ is 5 units what is the distance P'Q' ?

In the diagram the point P can move to different places around the dotted circle. Each position P takes will fix a corresponding position for P'. As P moves around on that circle what will P' do?

In the diagram the point P' can move to different places along the dotted line. Each position P' takes will fix a corresponding position for P. If P' moves along a straight line what does P do ?

Make your own pinhole camera for safe observation of the sun, and find out how it works.

How would you design the tiering of seats in a stadium so that all spectators have a good view?

Anamorphic art is used to create intriguing illusions - can you work out how it is done?