2D shapes and their properties

problem
LOGOsquares

Age

16 to 18

Challenge level

Ten squares form regular rings either with adjacent or opposite vertices touching. Calculate the inner and outer radii of the rings that surround the squares.
problem
Kissing

Age

16 to 18

Challenge level

Two perpendicular lines are tangential to two identical circles that touch. What is the largest circle that can be placed in between the two lines and the two circles and how would you construct it?
problem
Baby circle

Age

16 to 18

Challenge level

A small circle fits between two touching circles so that all three circles touch each other and have a common tangent? What is the exact radius of the smallest circle?
problem
Some(?) of the parts

Age

14 to 16

Challenge level

A circle touches the lines OA, OB and AB where OA and OB are perpendicular. Show that the diameter of the circle is equal to the perimeter of the triangle
problem
Chain of changes

Age

5 to 7

Challenge level

In this activity, shapes can be arranged by changing either the colour or the shape each time. Can you find a way to do it?
problem
Two by one

Age

7 to 11

Challenge level

An activity making various patterns with 2 x 1 rectangular tiles.
problem
Rectangles with dominoes

Age

5 to 7

Challenge level

Can you make a rectangle with just 2 dominoes? What about 3, 4, 5, 6, 7...?
problem
Four triangles puzzle

Age

5 to 11

Challenge level

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?
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Watch those wheels

Have you ever noticed the patterns in car wheel trims? These questions will make you look at car wheels in a different way!
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Lafayette

What mathematical words can be used to describe this floor covering? How many different shapes can you see inside this photograph?