MathDB

Let

P

be an arbitrary point inside triangle

ABC

, denote by

A_{1}

(different from

P

) the second intersection of line

AP

with the circumcircle of triangle

PBC

and define

B_{1},C_{1}

similarly. Prove that \left(1 \plus{} 2\cdot\frac {PA}{PA_{1}}\right)\left(1 \plus{} 2\cdot\frac {PB}{PB_{1}}\right)\left(1 \plus{} 2\cdot\frac {PC}{PC_{1}}\right)\geq 8.

Problem Statement