MathDB

2

Part of 2009 Portugal MO

Problems(2)

South African converse - Portuguese MO, Problem 2, 2009

Source:

8/29/2010
Points NN and MM are on the sides CDCD and BCBC of square ABCDABCD, respectively. The perimeter of triangle MCNMCN is equal to the double of the length of the square's side. Find ∠MAN\angle MAN.
geometryperimeterpower of a pointradical axisgeometry proposed
Hong Kong easy part - Portuguese MO, Problem 5, 2009

Source:

8/29/2010
Circumferences C1C_1 and C2C_2 have different radios and are externally tangent on point TT. Consider points AA on C1C_1 and BB on C2C_2, both different from TT, such that ∠BTA=90∘\angle BTA=90^{\circ}. What is the locus of the midpoints of line segments ABAB constructed that way?
geometry proposedgeometry