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How would the area change as one of the angles is changed?

You could try splitting the quadrilateral into two triangles. Can you find an expression for the length of the diagonal in two different ways?

 

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Just Touching

Three semi-circles have a common diameter, each touches the other two and two lie inside the biggest one. What is the radius of the circle that touches all three semi-circles?

Square World

P is a point inside a square ABCD such that PA= 1, PB = 2 and PC = 3. How big is angle APB ?

30-60-90 Polypuzzle

Re-arrange the pieces of the puzzle to form a rectangle and then to form an equilateral triangle. Calculate the angles and lengths.

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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