Let
be the centre of the inscribed circle of a triangle
Prove that for any point
where
and
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Let $Q$ be the centre of the inscribed circle of a triangle $ABC.$ Prove that for any point $P,$
$$a(PA)^2 + b(PB)^2 + c(PC)^2 = a(QA)^2 + b(QB)^2 + c(QC)^2 + (a + b + c)(QP)^2,$$
where $a = BC, b = CA$ and $c = AB.$
Školjka