MathDB

6

Part of 2019 South East Mathematical Olympiad

Problems(2)

the maximum of axy+byz+czx

Source: CSMO 2019 Grade 10 Problem 6

7/31/2019
Let a,b,ca,b,c be the lengths of the sides of a given triangle.If positive reals x,y,zx,y,z satisfy x+y+z=1,x+y+z=1, find the maximum of axy+byz+czx.axy+byz+czx.
algebra
Angle bisectors and parallel

Source: CSMO 2019 Grade 11 Problem 6

7/31/2019
In △ABC\triangle ABC, AB>ACAB>AC, the bisectors of ∠ABC,∠ACB\angle ABC, \angle ACB meet sides AC,ABAC,AB at D,ED,E respectively. The tangent at AA to the circumcircle of △ABC\triangle ABC intersects EDED extended at PP. Suppose that AP=BCAP=BC. Prove that BD∥CPBD\parallel CP.
geometry