MathDB

5

Part of 2013 Dutch IMO TST

Problems(2)

a + b + c >= \sqrt{\frac13 (a + 2)(b + 2)(c + 2)} when a,b,c>0 and abc=1

Source: Dutch IMO TST 2013 day 1 p5

8/29/2019
Let a,ba, b, and cc be positive real numbers satisfying abc=1abc = 1. Show that a+b+c≥13(a+2)(b+2)(c+2)a + b + c \ge \sqrt{\frac13 (a + 2)(b + 2)(c + 2)}
algebrainequalitiesDutch MOHigh school olympiad
Cyclic hexagon with two equal sides

Source: Netherlands IMO Team Selection Test 2013

10/21/2014
Let ABCDEFABCDEF be a cyclic hexagon satisfying AB⊥BDAB\perp BD and BC=EFBC=EF.Let PP be the intersection of lines BCBC and ADAD and let QQ be the intersection of lines EFEF and ADAD.Assume that PP and QQ are on the same side of DD and AA is on the opposite side.Let SS be the midpoint of ADAD.Let KK and LL be the incentres of △BPS\triangle BPS and △EQS\triangle EQS respectively.Prove that ∠KDL=900\angle KDL=90^0.
geometrycircumcirclesymmetrygeometry unsolved