AM-GM-HM inequalities

If
$$\frac{\sin^4x}2+\frac{\cos^4x}3=\frac15,$$
then

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

Which one of the following statements is correct?

Which one of the following statements is correct?

Which one of the following statements is correct?