projections of a point of a triangle onto triangle sides, prove the inequality with triangle area

Question

Let $P$ be a point of a triangle $ABC$.

Let $K,L,M$ be the projections of $P$ onto $BC,CA,AB$ respectively.

Let $Q$ be the circumcentre of $\triangle KLM$ and let $q$ be the circumradius of $\triangle KLM$.

Prove that $[ABC]\ge 3q\cdot\sqrt{3q^2-QP^2}$.