MathDB

3

Part of 2018 Puerto Rico Team Selection Test

Problems(2)

<BKC=<CDB if MA x CD = MB x LD Puerto Rico OMCC TST 2018.3

Source:

9/16/2021
Let MM be the point of intersection of diagonals ACAC and BDBD of the convex quadrilateral ABCDABCD. Let KK be the point of intersection of the extension of side ABAB (beyondAA) with the bisector of the angle ACDACD. Let LL be the intersection of KCKC and BDBD. If MA⋅CD=MB⋅LDMA \cdot CD = MB \cdot LD, prove that the angle BKCBKC is equal to the angle CDBCDB.
equal anglesgeometry
sum of all elements of B is divisible by m Puerto Rico Ibero IMO TST 2018.3

Source:

9/16/2021
Let AA be a set of mm positive integers where m≥1m\ge 1. Show that there exists a nonempty subset BB of AA such that the sum of all the elements of BB is divisible by mm.
number theorydivisiblesivides