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
A 1 metre cube has one face on the ground and one face against a
wall. A 4 metre ladder leans against the wall and just touches the
cube. How high is the top of the ladder above the ground?
The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?
ABC and DEF are equilateral triangles of side
3 and 4 respectively. Construct an equilateral triangle whose area
is the sum of the area of ABC and DEF .
Does this work for any whole number side lengths?
If not, under what circumstances does it work?
What if the lengths of the sides of the triangles had been
a and b instead of 3 and 4, can you construct an
equilateral triangle whose area is the sum of the areas of
ABC and DEF ? What is the new area?