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# Cyclic Quad Jigsaw

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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:

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

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.

A kite shaped lawn consists of an equilateral triangle ABC of side 130 feet and an isosceles triangle BCD in which BD and CD are of length 169 feet. A gardener has a motor mower which cuts strips of grass exactly one foot wide and wishes to cut the entire lawn in parallel strips. What is the minimum number of strips the gardener must mow?

What can you say about the lengths of the sides of a quadrilateral whose vertices are on a unit circle?