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A straight line through the vertex `P` of a triangle `P Q R` intersects the side `Q R` at the points `S` and the cicumcircle of the triangle `P Q R` at the point `Tdot` If `S` is not the center of the circumcircle, then `1/(P S)+1/(S T)<2/(sqrt(Q SxxS R))` `1/(P S)+1/(S T)>2/(sqrt(Q SxxS R))` `1/(P S)+1/(S T)<4/(Q R)` `1/(P S)+1/(S T)>4/(Q R)`

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