In triangle
- Show that
and are similar. (1 mark) - Show that
. (1 mark)
- From
, a line perpendicular to is drawn to meet at , forming the right-angled triangle . A new quadrant is constructed in triangle touching side at . The process is then repeated indefinitely.
- Show that the limiting sum of the areas of all the quadrants is
(4 marks)
- Hence, or otherwise, show that
. (1 mark)