MathDB

4

Part of 2017 NMTC Junior

Problems(1)

Inequality and Geometry

Source: NMTC 2017 Junior P4

10/28/2017
a) a,b,c,da,b,c,d are positive reals such that abcd=1abcd=1. Prove that ∑cyc1+ab1+a≥4.\sum_{cyc} \frac{1+ab}{1+a}\geq 4. (b)In a scalene triangle ABCABC, ∠BAC=120∘\angle BAC =120^{\circ}. The bisectors of angles A,B,CA,B,C meets the opposite sides in P,Q,RP,Q,R respectively. Prove that the circle on QRQR as diameter passes through the point PP.
inequalitiesgeometry