MathDB

2

Part of 2001 Cuba MO

Problems(2)

<BKC = <CDB if MA x MC + MA x CD = MB xMD

Source: 2001 Cuba MO 1.2

9/15/2024
Let MM be the point of intersection of the diagonals ACAC and BDBD of the convex quadrilateral ABCDABCD. LetK K be the intersection point of the extension of side ABAB (from AA) with the bisector of the ∠ACD\angle ACD. If MA⋅MC+MA⋅CD=MB⋅MDMA \cdot MC + MA \cdot CD = MB\cdot MD , prove that ∠BKC=∠CDB\angle BKC = \angle CDB.
geometryequal angles
AP_|_MK if MC = KD in square ABCD - 2001 Cuba MO 2.2

Source:

9/15/2024
Let ABCDABCD be a square. On the sides BCBC and CDCD the points MM and KK respectively, so that MC=KDMC = KD. Let PP the intersection point of of segments MDMD and BKBK. Prove that AP⊥MKAP \perp MK.
geometrysquareperpendicular