JEE Main & Advanced
Sample Paper
JEE Main Sample Paper-8
question_answer
A triangle ABC satisfies the relation \[2\sec 4C\]\[+{{\sin }^{2}}\text{ }2A+\sqrt{\sin B}=0\] and a point P is taken on the longest side of the triangle such that it divides the side in the ratio 1 : 3. Let Q and R be the circumcentre and orthocentre of A \[\Delta ABC.\]If \[PQ:QR:RP=1:\alpha :\beta ,\]then the value of \[{{\alpha }^{2}}+{{\beta }^{2}}.\]