« Vrati se
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.

Slični zadaci

#NaslovOznakeRj.KvalitetaTežina
1662IMO Shortlist 1985 problem 211
1677IMO Shortlist 1986 problem 141
1678IMO Shortlist 1986 problem 150
1710IMO Shortlist 1988 problem 30
1722IMO Shortlist 1988 problem 150
1737IMO Shortlist 1988 problem 300