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Vn Mathematics
The auxiliary lines in the picture give important hints.

Proof: connect AO and extend BC to m, connect VM,

Because OA1/va, A 1 is on VM, OA1/va = om/am;

Similarly, connect BO, extend AC to N, and connect VN; Connect CO and extend AB to p, connect VP,

Then OB 1/VB = ON/BN, OC 1/VC = OP/CP,

In the triangle ABC, OM/AM = SBOC/SABC (because the bottom is BC).

Similarly ON/BN = SAOC/SABC, OP/CP = SAOB/SABC,

The result is OA1/va+ob1/VB+oc1/VC.

= OM/AM+ON/VN+OP/CP

= SBOC/ SABC +SAOC/ SABC +SAOB/ SABC

= (SBOC+SAOC+SAOB)/SABC

= SABC/SABC

= 1 is a fixed value.