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7

Part of 2015 Bangladesh Mathematical Olympiad

Problems(1)

Bangladesh Mathematical Olympiad 2015, Secondary, P7

Source:

3/31/2015
In triangle △ABC\triangle ABC, the points A′,B′,C′A', B', C' are on sides BC,AC,ABBC, AC, AB respectively. Also, AA′,BB′,CC′AA', BB', CC' intersect at the point OO(they are concurrent at OO). Also, AOOA′+BOOB′+COOC′=92\frac {AO}{OA'}+\frac {BO}{OB'}+\frac {CO}{OC'} = 92. Find the value of AOOA′×BOOB′×COOC′\frac {AO}{OA'}\times \frac {BO}{OB'}\times \frac {CO}{OC'}.
national olympiadgeometryalgebraareaCevas Theorem