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The tangent at any point P of a circle x...

The tangent at any point `P` of a circle `x^2 + y^2 = a^2` meets the tangent at a fixed point `A (a, 0)` in `T` and `T` is joined to `B`, the other end of the diameter through `A,` prove that the locus of the intersection of `AP` and `BT` is an ellipse whose eccentricity is `1/sqrt2`

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