MathDB

3

Part of 2012 Bosnia And Herzegovina - Regional Olympiad

Problems(3)

Regional Olympiad - FBH 2012 Grade 10 Problem 3

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2012

9/25/2018
Quadrilateral ABCDABCD is cyclic. Line through point DD parallel with line BCBC intersects CACA in point PP, line ABAB in point QQ and circumcircle of ABCDABCD in point RR. Line through point DD parallel with line ABAB intersects ACAC in point SS, line BCBC in point TT and circumcircle of ABCDABCD in point UU. If PQ=QRPQ=QR, prove that ST=TUST=TU
geometrycircumcircle
Regional Olympiad - FBH 2012 Grade 9 Problem 3

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2012

9/25/2018
Find remainder when dividing upon 20122012 number A=1⋅2+2⋅3+3⋅4+...+2009⋅2010+2010⋅2011A=1\cdot2+2\cdot3+3\cdot4+...+2009\cdot2010+2010\cdot2011
remaindernumber theory
Regional Olympiad - FBH 2012 Grade 11 Problem 3

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2012

9/25/2018
Prove tha number 19⋅8n+1719 \cdot 8^n +17 is composite for every positive integer nn
number theoryComposite