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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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Long Short

A quadrilateral inscribed in a unit circle has sides of lengths s1, s2, s3 and s4 where s1 ≤ s2 ≤ s3 ≤ s4. Find a quadrilateral of this type for which s1= sqrt2 and show s1 cannot be greater than sqrt2. Find a quadrilateral of this type for which s2 is approximately sqrt3and show that s2 is always less than sqrt3. Find a quadrilateral of this type for which s3 is approximately 2 and show that s2 is always less than 2. Find a quadrilateral of this type for which s4=2 and show that s4 cannot be greater than 2.

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Diagonals for Area

Prove that the area of a quadrilateral is given by half the product of the lengths of the diagonals multiplied by the sine of the angle between the diagonals.

Cyclic Quad Jigsaw

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Someone showed me this picture of a quadrilateral made by joining together five smaller quadrilaterals.

Cyclic

It made me think about special cases...

Could I draw a version of this image where all five of the smaller quadrilaterals are cyclic? I tried it out and have tried to capture what I did, and what the question was that it made me want to answer, in the video below:

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Can you convince us that the largest quadrilateral is also cyclic?