Area - circles, sectors and segments

There are 32 NRICH Mathematical resources connected to Area - circles, sectors and segments
Giant Holly Leaf
problem

Giant Holly Leaf

Age
14 to 16
Challenge level
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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).
Mean Geometrically
problem

Mean Geometrically

Age
16 to 18
Challenge level
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A and B are two points on a circle centre O. Tangents at A and B cut at C. CO cuts the circle at D. What is the relationship between areas of ADBO, ABO and ACBO?