MathDB

1

Part of 2016 Bulgaria JBMO TST

Problems(2)

AB <AD + CD , <BAC < <DCB, < BOD = <ADC = a , ABCD cyclic

Source: 2016 Bulgaria JBMO TST 1.1

8/11/2020
The quadrilateral ABCDABCD, in which ∠BAC<∠DCB\angle BAC < \angle DCB , is inscribed in a circle cc, with center OO. If ∠BOD=∠ADC=α\angle BOD = \angle ADC = \alpha. Find out which values of α\alpha the inequality AB<AD+CDAB <AD + CD occurs.
geometrygeometric inequalityanglescyclic quadrilateral
Algebra proposed

Source: Bulgaria 2016 JTST P1 day 2

8/27/2019
a,b,c,d,e,f a,b,c,d,e,f are real numbers. It is true that: a+b+c+d+e+f=20 a+b+c+d+e+f=20 (a−2)2+(b−2)2+...+(f−2)2=24 (a-2)^2+(b-2)^2+...+(f-2)^2=24 Find the maximum value of d.
algebra proposedalgebra