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Given a square ABCD of sides 10 cm, and using the corners as centres, construct four quadrants with radius 10 cm each inside the square. The four arcs intersect at P, Q, R and S. Find the area enclosed by PQRS.

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Darts and Kites

A rhombus PQRS has an angle of 72 degrees. OQ = OR = OS = 1 unit. Find all the angles, show that POR is a straight line and that the side of the rhombus is equal to the Golden Ratio.

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A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?

Bendy Quad

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

Four rods are hinged at their ends to form a convex quadrilateral with sides of length $3$, $4$, $5$ and $6$ (in that order). Investigate the different shapes that the quadrilateral can take.

What are all the possible values of the angles if the quadrilateral is convex?

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