MathDB

2

Part of 2014 Dutch IMO TST

Problems(2)

Prove that AB=CE

Source: Dutch IMO TST I Problem 2

7/17/2014
Let △ABC\triangle ABC be a triangle. Let MM be the midpoint of BCBC and let DD be a point on the interior of side ABAB. The intersection of AMAM and CDCD is called EE. Suppose that ∣AD∣=∣DE∣|AD|=|DE|. Prove that ∣AB∣=∣CE∣|AB|=|CE|.
trigonometrygeometrygeometric transformationreflectionprojective geometrytrig identitiesLaw of Sines
Maximum number elements in A U B

Source: Dutch IMO TST II Problem 2

7/17/2014
The sets AA and BB are subsets of the positive integers. The sum of any two distinct elements of AA is an element of BB. The quotient of any two distinct elements of BB (where we divide the largest by the smallest of the two) is an element of AA. Determine the maximum number of elements in A∪BA\cup B.
number theory unsolvednumber theory