Construction of tangents

In order to find the tangents from a point P to a conic, we choose two lines through P which intersect the conic. Then we construct the harmonic conjugates F1 and F2 of P with respect to the two pairs G1H1, and G2H2. The line connecting F1 and F2 is the polar to P and intersects the conic in the contact points of the tangents through P.  

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