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Iran MO (3rd Round)
2002 Iran MO (3rd Round)
21
21
Part of
2002 Iran MO (3rd Round)
Problems
(1)
radii are equal
Source: Iranian National Olympiad (3rd Round) 2002
10/5/2006
Excircle of triangle
A
B
C
ABC
A
BC
corresponding vertex
A
A
A
, is tangent to
B
C
BC
BC
at
P
P
P
.
A
P
AP
A
P
intersects circumcircle of
A
B
C
ABC
A
BC
at
D
D
D
. Prove
r
(
P
C
D
)
=
r
(
P
B
D
)
r(PCD)=r(PBD)
r
(
PC
D
)
=
r
(
PB
D
)
whcih
r
(
P
C
D
)
r(PCD)
r
(
PC
D
)
and
r
(
P
B
D
)
r(PBD)
r
(
PB
D
)
are inradii of triangles
P
C
D
PCD
PC
D
and
P
B
D
PBD
PB
D
.
geometry
circumcircle
ratio
perimeter
geometry proposed