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This problem offers the opportunity to practise calculating arc lengths, working in terms of $\pi$, and calculating interior angles of regular polygons. It also provides an opportunity to generalise from simple examples, and to explain patterns in terms of the underlying structure of the problem.
This printable worksheet may be useful: Triangles and Petals
Start by showing the animation of the triangle rotating around another triangle. Then hide the animation and ask learners to sketch what they saw. Show the animation once more so they can confirm what they saw.
What angles do you know? What angles can you work out?
An Unusual Shape offers opportunities to visualise sectors of circles and to consider simple loci.
Construct a proof for the formula for finding the perimeter of a flower with a regular $n$-sided polygon at its centre.
Find the perimeter and area of a holly leaf that will not lie flat (it has negative curvature with 'circles' having circumference greater than 2πr).
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.
A white cross is placed symmetrically in a red disc with the central square of side length sqrt 2 and the arms of the cross of length 1 unit. What is the area of the disc still showing?