# Coordinates

Geometry Level 5

Coordinates of the vertices $$B$$ and $$C$$ of a triangle $$ABC$$ are $$(2,0)$$ and $$(8,0)$$ respectively. The vertex $$A$$ is varying in such a way that :

$$4tan\dfrac { B }{ 2 } tan\dfrac { C }{ 2 } = 1$$

The locus of $$A$$ is an ellipse. Then find out value of the product of the semi-major and semi-minor axis

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