2D shapes and their properties

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.

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?

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?

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

Arrange the shapes in a line so that you change either colour or shape in the next piece along. Can you find several ways to start with a blue triangle and end with a red circle?

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

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

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?