equal segments in a parallelogram given, angle wanted
Source: Dutch NMO 2017 p2
September 7, 2019
geometryparallelogramanglesequal segments
Problem Statement
A parallelogram with has been given. A point lies on line segment in such a way that . The (extended) line intersects line segment in . Line is the angle bisector of angle . Determine the size of angle .
[asy]
unitsize (3 cm);pair A, B, C, D, E, F;D = (0,0);
A = dir(250);
B = dir(290);
C = B + D - A;
E = extension((A + D)/2, (A + D)/2 + rotate(90)*(A - D), B, D);
F = extension(A, E, B, C);draw(A--B--C--D--cycle);
draw(A--F--D--B);dot("", A, SW);
dot("", B, SE);
dot("", C, NE);
dot("", D, NW);
dot("", E, S);
dot("", F, SE);
[/asy]