angle chasing in a quadrilateral with 2 parallel sides, few equal segments
Source: Dutch NMO 2013 p3
September 6, 2019
parallelgeometryanglesdiagonals
Problem Statement
The sides and of a quadrilateral are parallel and the diagonals intersect in . For this quadrilateral and hold. Furthermore is the angular bisector of angle . Determine the size of angle .[asy]
unitsize(1 cm);pair A, B, C, D, O;D = (0,0);
B = 3*dir(180 + 72);
C = 3*dir(180 + 72 + 36);
A = extension(D, D + (1,0), C, C + dir(180 - 36));
O = extension(A, C, B, D);draw(A--B--C--D--cycle);
draw(B--D);
draw(A--C);dot("", A, N);
dot("", B, SW);
dot("", C, SE);
dot("", D, N);
dot("", O, E);
[/asy]Attention: the figure is not drawn to scale.