MathDB

1

Part of 2001 Turkey MO (2nd round)

Problems(2)

Turkey NMO 2001 Problem 1

Source: Turkey NMO 2001 Problem 1

9/30/2011
Let ABCDABCD be a convex quadrilateral. The perpendicular bisectors of the sides [AD][AD] and [BC][BC] intersect at a point PP inside the quadrilateral and the perpendicular bisectors of the sides [AB][AB] and [CD][CD] also intersect at a point QQ inside the quadrilateral. Show that, if ∠APD=∠BPC\angle APD = \angle BPC then ∠AQB=∠CQD\angle AQB = \angle CQD
geometrycircumcircletrapezoidgeometry proposed
Turkey NMO 2001 Problem 4, Diophant Equation

Source: Turkey NMO 2001 Problem 4

9/30/2011
Find all ordered triples of positive integers (x,y,z)(x,y,z) such that 3x+11y=z23^{x}+11^{y}=z^{2}
number theory proposednumber theory