MathDB

1

Part of 2007 Iran MO (2nd Round)

Problems(2)

Iran NMO 2007 (Second Round) - Problem1

Source:

9/22/2010
In triangle ABCABC, ∠A=90∘\angle A=90^{\circ} and MM is the midpoint of BCBC. Point DD is chosen on segment ACAC such that AM=ADAM=AD and PP is the second meet point of the circumcircles of triangles ΔAMC,ΔBDC\Delta AMC,\Delta BDC. Prove that the line CPCP bisects ∠ACB\angle ACB.
geometrycircumcirclegeometry proposed
Iran NMO 2007 (Second Round) - Problem4

Source:

9/22/2010
Prove that for every positive integer nn, there exist nn positive integers such that the sum of them is a perfect square and the product of them is a perfect cube.
number theory proposednumber theory