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Cyclic Quad Jigsaw

Age 14 to 16 Challenge Level:

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


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?