MathDB

2

Part of 2021 Korea Winter Program Practice Test

Problems(2)

function

Source: 2021 Korea Winter Program Practice Test

2/8/2021
Find all functions f:R+→R+f:R^+\rightarrow R^+ such that for all positive reals xx and yy 4f(x+yf(x))=f(x)f(2y)4f(x+yf(x))=f(x)f(2y)
functionalgebra
<XAY >=60

Source: 2021 Korea Winter Program Test1 Day1 #2

2/5/2021
Let ABCABC be a triangle with ∠A=60∘\angle A=60^{\circ}. Point D,ED, E in lines AB→,AC→\overrightarrow{AB}, \overrightarrow{AC} respectively satisfies DB=BC=CEDB=BC=CE. (A,B,DA,B,D lies on this order, and A,C,EA,C,E likewise) Circle with diameter BCBC and circle with diameter DEDE meets at two points X,YX, Y. Prove that ∠XAY≥60∘\angle XAY\ge 60^{\circ}
geometry