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National and Regional Contests
Japan Contests
Japan MO Finals
2003 Japan MO Finals
1
find the angle
find the angle
Source: Japanese MO 2003, problem 1
April 20, 2007
geometry
circumcircle
angle bisector
geometry unsolved
Problem Statement
A point
P
P
P
lies in
△
A
B
C
\triangle ABC
△
A
BC
. The lines
B
P
,
C
P
BP,CP
BP
,
CP
meet
A
C
,
A
B
AC,AB
A
C
,
A
B
at
Q
,
R
Q,R
Q
,
R
respectively. Given that
A
R
=
R
B
=
C
P
,
C
Q
=
P
Q
AR=RB=CP, CQ=PQ
A
R
=
RB
=
CP
,
CQ
=
PQ
, find
∠
B
R
C
\angle BRC
∠
BRC
.
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