jee-advanced 2008 Q7

jee-advanced · India · paper1 Circles Chord Length and Chord Properties
A straight line through the vertex $P$ of a triangle $P Q R$ intersects the side $Q R$ at the point $S$ and the circumcircle of the triangle $P Q R$ at the point $T$. If $S$ is not the centre of the circumcircle, then
(A) $\frac { 1 } { P S } + \frac { 1 } { S T } < \frac { 2 } { \sqrt { Q S \times S R } }$
(B) $\frac { 1 } { P S } + \frac { 1 } { S T } > \frac { 2 } { \sqrt { Q S \times S R } }$
(C) $\frac { 1 } { P S } + \frac { 1 } { S T } < \frac { 4 } { Q R }$
(D) $\frac { 1 } { P S } + \frac { 1 } { S T } > \frac { 4 } { Q R }$
(B) and (D)
A straight line through the vertex $P$ of a triangle $P Q R$ intersects the side $Q R$ at the point $S$ and the circumcircle of the triangle $P Q R$ at the point $T$. If $S$ is not the centre of the circumcircle, then\\
(A) $\frac { 1 } { P S } + \frac { 1 } { S T } < \frac { 2 } { \sqrt { Q S \times S R } }$\\
(B) $\frac { 1 } { P S } + \frac { 1 } { S T } > \frac { 2 } { \sqrt { Q S \times S R } }$\\
(C) $\frac { 1 } { P S } + \frac { 1 } { S T } < \frac { 4 } { Q R }$\\
(D) $\frac { 1 } { P S } + \frac { 1 } { S T } > \frac { 4 } { Q R }$