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MK = KN wanted, angle bisectors from A related

Source: TOT 466 1995 Autumn J O4 - Tournament of Towns

July 9, 2024

geometryangle bisectorequal segments

Problem Statement

From the vertex

A

of a triangle

ABC

, three segments are drawn: the bisectors

AM

and

AN

of its interior and exterior angles and the tangent

AK

to the circumscribed circle of the triangle (the points

M

K

and

N

lie on the line

BC

). Prove that

MK = KN

.
(I Sharygin)