MathDB

2

Part of 1998 Iran MO (3rd Round)

Problems(2)

Show that the angles are equal

Source: Iran Third Round MO 1998, Exam 1, P2

7/23/2009
Let ABCDABCD be a convex pentagon such that ∠DCB=∠DEA=90∘, and DC=DE.\angle DCB = \angle DEA = 90^\circ, \ \text{and} \ DC=DE. Let FF be a point on AB such that AF:BF=AE:BCAF:BF=AE:BC. Show that ∠FEC=∠BDC, and ∠FCE=∠ADE.\angle FEC= \angle BDC, \ \text{and} \ \angle FCE= \angle ADE.
geometrycyclic quadrilateralgeometry unsolved
Convex Hexagon

Source: Iran Third Round MO 1998, Exam 4, P2

10/31/2010
Let ABCDEFABCDEF be a convex hexagon such that AB=BC,CD=DEAB = BC, CD = DE and EF=FAEF = FA. Prove that ABBE+CDAD+EFCF≥32.\frac{AB}{BE}+\frac{CD}{AD}+\frac{EF}{CF} \geq \frac{3}{2}.
inequalitiesgeometry unsolvedgeometry