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Just Touching

Three semi-circles have a common diameter, each touches the other two and two lie inside the biggest one. What is the radius of the circle that touches all three semi-circles?

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Bendy Quad

Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.

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Biggest Bendy

Four rods are hinged at their ends to form a quadrilateral with fixed side lengths. Show that the quadrilateral has a maximum area when it is cyclic.

Hexy-metry

Stage: 4 and 5 Challenge Level: Challenge Level:2 Challenge Level:2

Make cards from the images in this document .
Do they help you to make connections?
Can you arrange them in ways that help you to see some of the properties of the problem image?