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Triangles are formed by pairs of tangent...

Triangles are formed by pairs of tangents drawn from any point on the ellipse
` a^(2) x^(2) + b^(2) y^(2) = ( a^(2) + b^(2))^(2)` to the ellipse ` ( x^(2))/( a^(2)) + (y^(2))/(b^(2))` = 1
and their chord of contact. Prove that the orthocentre of each such triangle lies on the ellipse.

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