MathDB

Let

ABC

be an acute-angled triangle with

AB<AC<BC

and

c(O,R)

the circumscribed circle. Let

D, E

be points in the small arcs

AC, AB

respectively. Let

K

be the intersection point of

BD,CE

and

N

the second common point of the circumscribed circles of the triangles

BKE

and

CKD

. Prove that

A, K, N

are collinear if and only if

K

belongs to the symmedian of

ABC

passing from

A

Problem Statement