COMC 1997 #1
Source:
June 8, 2017
Problem Statement
In triangle ABC, A equals 120 degrees. A point D is inside the triangle such that DBC = 2 ABD and DCB = 2 ACD. Determine the measure, in degrees, of BDC.
[asy]pair A = (5,4);
pair B = (0,0);
pair C = (10,0);
pair D = (5,2.5) ;
draw(A--B);
draw(B--C);
draw(C--A);
draw (B--D--C);
label ("A", A, dir(45));
label ("B", B, dir(45));
label ("C", C, dir(45));
label ("D", D, dir(45));[/asy]