You may also like

problem icon

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.

problem icon

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.

problem icon


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


Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

square ABCD of sides 10 cm, with 4 quadrants of radius 10cm constructed using the corners of the square as centres.

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 $PQRS$.