Doubly Trisected Triangle

Geometry Level 5

Triangle ABC has A=40\angle A = 40^{\circ}, B=60\angle B = 60^{\circ}, C=80\angle C = 80^{\circ}. Points M,NM,N trisect the side BCBC and points P,QP,Q trisect the side ACAC. The lines AM,AN,BP,BQAM, AN, BP, BQ intersect at the points S,T,U,VS,T,U,V as shown in the figure below, dividing the triangle into 9 regions. Determine the smallest possible value of [ABC]+[STUV][ABC] + [STUV] such that both [ABC][ABC] and [STUV][STUV] are positive integers.

Details and assumptions

[PQRS][PQRS] refers to the area of figure PQRSPQRS.

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