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Rhombus ABCD of side 1 - find the measures of the angles

Source: Romanian IMO Team Selection Test TST 2003, problem 14

September 24, 2005

geometryrhombusgeometry proposed

Problem Statement

Given is a rhombus

ABCD

of side 1. On the sides

BC

and

CD

we are given the points

M

and

N

respectively, such that

MC+CN+MN=2

and

2\angle MAN = \angle BAD

. Find the measures of the angles of the rhombus. Cristinel Mortici