Here are 2 questions which none of the students in our institution
could solve :

D is a point on the circumcircle of triangle ABC in which AB = AC
such that B and D are on oppostie sides of the line AC. If CD is
produced to a point E such that CE = BD, proove that AB = AE.

Bisectors of angles A, B C interesct the circumcircle at D, E, F
respectivley, proove that the angles of the triangle are 90-A/2, 90-
B/2, 90-C/2 respectivley.

Thank you