Stage: 5 Challenge Level: 
$O$ is the centre of a circle with $A$ and $B$ two points NOT on a diameter. The tangents to $A$ and $B$ cut at $C$. $CO$ cuts the circle at $D$ and a tangent through $D$ cuts $AC$ and $BC$ at $E$ and $F$.
What is the relationship between area of $ADBO$ and the areas of $ABO$ and $ACBO$?
Graph sketching. Geometric mean. Area. Long problems. Pythagoras' theorem. Arcs, sectors and segments. Symmetry. Quadratic equations. Surds. Index notation/Indices.
Published March 1999.
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