Geometry: Secants and Inequalities

XAT 2011 · QADI · Hard · Geometry

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A straight line through point P of a triangle PQR intersects the side QR at the point S and the circumcircle of the triangle PQR at the point T. If S is not the centre of the circumcircle, then which of the following is true?

  1. A.

    \frac{1}{PS} + \frac{1}{ST} < \frac{2}{\sqrt{QS \cdot QR}}

  2. B.

    \frac{1}{PS} + \frac{1}{ST} < \frac{4}{QR}

  3. C.

    \frac{1}{PS} + \frac{1}{ST} > \frac{1}{\sqrt{QS \cdot QR}}

  4. D.

    \frac{1}{PS} + \frac{1}{ST} > \frac{4}{QR}

  5. E.

    None of the above

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