MathDB

2020 IGO Advanced P1

Source: 7th Iranian Geometry Olympiad (Advanced) P1

November 4, 2020

geometryIGOiranian geometry olympiadmidpoints

Problem Statement

Let

M,N,P

be midpoints of

BC,AC

and

AB

of triangle

\triangle ABC

respectively.

E

and

F

are two points on the segment

\overline{BC}

so that

\angle NEC = \frac{1}{2} \angle AMB

and

\angle PFB = \frac{1}{2} \angle AMC

. Prove that

AE=AF

. Proposed by Alireza Dadgarnia