Mongolian Mathematical Olympiad

Question

Let M be an arbitrary point on the side AB of regular triangle ABC. If one erects regular triangle AMN outwardly, lines BN and AC intersect at point D. Denote K the intersection point of lines AN and CM. Find the angle ADK.

Accepted Answer

Since triangles ABC and MAN are regular, BAC = 60^ = MAN NAD = 60^. . arrayl AC = AB AM = AN CAM = MAN = 60^ CMA = BAN KCA = DBA. array . arrayl AC = AB AM = AN CAM = MAN = 60^ array we get CAK = BAD. So AK = AD and KAD = 60^. It follows the triangle AKD is regular and hence we have KDA = 60^.