What happens to the perimeter of triangle ABC as the two smaller
circles change size and roll around inside the bigger circle?
Two semicircle sit on the diameter of a semicircle centre O of
twice their radius. Lines through O divide the perimeter into two
parts. What can you say about the lengths of these two parts?
Show that for any triangle it is always possible to construct 3
touching circles with centres at the vertices. Is it possible to
construct touching circles centred at the vertices of any polygon?
The triangle OPA has a vertex O at the origin and OA along
the x axis, such that P has coordinates (x, y)
and A has coordinates (2x, 0). By moving the position
of the point P infinitely many isosceles triangles can be
formed all having an area of 12 square units. What is the
locus of P such that the area of the triangle OPA is 12
square units? In the Java applet below, the point P is
controlled by sliding the red point along the red line. If
the red point disappears from view, simply press reload.