Class 11

Math

Algebra

Sequences and Series

A straight line through the vertex $P$ 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

- $PS1 +ST1 <QS×SR 2 $
- $PS1 +ST1 >QS×SR 2 $
- $PS1 +ST1 <QR4 $
- $PS1 +ST1 >QR4 $

We have $PS×ST=QS×SR$

$⇒2PS1 +ST1 >PS1 ×ST1 $

$⇒PS1 +ST1 >QS×SR 2 $

Also

$2QS+SR >QR2 $

$⇒PS1 +ST1 >QR4 $