A straight line through the vertex of a intersects the side at and the circumcircle of at

MATHEMATICS · Single correct · ICSE · Mathematics · Geometry · Geometry

Problem

A straight line through the vertex

P

of a

\triangle PQR

intersects the side

QR

S

and the circumcircle of

\triangle PQR

T

. If

S

is not the centre of the circumcircle, then (1)

\frac{1}{PS}+\frac{1}{ST}<\frac{2}{\sqrt{QS\times SR}}

(2)

\frac{1}{PS}+\frac{1}{ST}>\frac{2}{\sqrt{QS\times SR}}

(3)

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

(4)

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