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National and Regional Contests
China Contests
(China) National High School Mathematics League
2017 China Second Round Olympiad
1
1
Part of
2017 China Second Round Olympiad
Problems
(1)
2017 China Second Round Test 2 Olympiad Problem 1
Source: 2017 China Second Round Test 2 Olympiad Problem 1
9/10/2017
Given an isocleos triangle
A
B
C
ABC
A
BC
with equal sides
A
B
=
A
C
AB=AC
A
B
=
A
C
and incenter
I
I
I
.Let
Γ
1
\Gamma_1
Γ
1
be the circle centered at
A
A
A
with radius
A
B
AB
A
B
,
Γ
2
\Gamma_2
Γ
2
be the circle centered at
I
I
I
with radius
B
I
BI
B
I
.A circle
Γ
3
\Gamma_3
Γ
3
passing through
B
,
I
B,I
B
,
I
intersects
Γ
1
\Gamma_1
Γ
1
,
Γ
2
\Gamma_2
Γ
2
again at
P
,
Q
P,Q
P
,
Q
(different from
B
B
B
) respectively.Let
R
R
R
be the intersection of
P
I
PI
P
I
and
B
Q
BQ
BQ
.Show that
B
R
⊥
C
R
BR \perp CR
BR
⊥
CR
.
geometry
incenter