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# Mean Geometrically

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### Approximating Pi

### Spokes

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Age 16 to 18

Challenge Level

$O$ is the centre of a circle with $A$ and $B$ two points NOT on a diameter. The tangents to $A$ and $B$ intersect 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 $ACBO$?

By inscribing a circle in a square and then a square in a circle find an approximation to pi. By using a hexagon, can you improve on the approximation?

Draw three equal line segments in a unit circle to divide the circle into four parts of equal area.