A and B are two points on a circle centre O. Tangents at A and B
cut at C. CO cuts the circle at D. What is the relationship between
areas of ADBO, ABO and ACBO?
Three triangles ABC, CBD and ABD (where D is a point on AC) are all
isosceles. Find all the angles. Prove that the ratio of AB to BC is
equal to the golden ratio.
The square ABCD is split into three triangles by the lines BP and
CP. Find the radii of the three inscribed circles to these
triangles as P moves on AD.