MathDB
Problems
Contests
National and Regional Contests
Austria Contests
Austrian MO Regional Competition
2008 Regional Competition For Advanced Students
3
39th Austrian Mathematical Olympiad 2008
39th Austrian Mathematical Olympiad 2008
Source: round1, problem3
February 10, 2009
geometry
circumcircle
geometry unsolved
Problem Statement
Given is an acute angled triangle
A
B
C
ABC
A
BC
. Determine all points
P
P
P
inside the triangle with
1
≤
∠
A
P
B
∠
A
C
B
,
∠
B
P
C
∠
B
A
C
,
∠
C
P
A
∠
C
B
A
≤
2
1\leq\frac{\angle APB}{\angle ACB},\frac{\angle BPC}{\angle BAC},\frac{\angle CPA}{\angle CBA}\leq2
1
≤
∠
A
CB
∠
A
PB
,
∠
B
A
C
∠
BPC
,
∠
CB
A
∠
CP
A
≤
2
Back to Problems
View on AoPS