MathDB

4

Part of 2007 Peru MO (ONEM)

Problems(1)

equal angles wanted, starting with a rhombus ABCD with equil. ABD and BCD

Source: Peru MO 2007 level 3 p4

5/16/2019
Let ABCDABCD be rhombus ABCDABCD where the triangles ABDABD and BCDBCD are equilateral. Let MM and NN be points on the sides BCBC and CDCD, respectively, such that ∠MAN=30o\angle MAN = 30^o. Let XX be the intersection point of the diagonals ACAC and BDBD. Prove that ∠XMN=∠ DAM\angle XMN = \angle\ DAM and ∠XNM=∠BAN\angle XNM = \angle BAN.
geometryrhombusEquilateralequal angles