Got this proof from the internet. www.ddhw.com As before, ABC is the triangle, BY, CZ the bisectors of B, C, with Y on AC, Z on AB. We have BY = CZ. Let E be the intersection of BY and CZ. Connect A, E. Find the point D outside of edge AB so that BD = AZ and DY = AC. www.ddhw.com So triangle DBY is congruent with AZC. Let the bisector of A, D, B, Y are concyclic ( www.ddhw.com Then A, D, F, E are concyclic ( Since AE = DF (DBY congruent with AZC) , we have AD // EF. Therefore, www.ddhw.com
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