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IMO Longlists
1986 IMO Longlists
31
31
Part of
1986 IMO Longlists
Problems
(1)
PQ passes through the circumcenter of ABC
Source:
8/29/2010
Let
P
P
P
and
Q
Q
Q
be distinct points in the plane of a triangle
A
B
C
ABC
A
BC
such that
A
P
:
A
Q
=
B
P
:
B
Q
=
C
P
:
C
Q
AP : AQ = BP : BQ = CP : CQ
A
P
:
A
Q
=
BP
:
BQ
=
CP
:
CQ
. Prove that the line
P
Q
PQ
PQ
passes through the circumcenter of the triangle.
geometry
circumcircle
ratio
geometry unsolved