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Problems
Contests
International Contests
Baltic Way
2019 Baltic Way
11
11
Part of
2019 Baltic Way
Problems
(1)
Intersection of two circles in an isosceles triangle
Source: 2019 Baltic Way P11
11/18/2019
Let
A
B
C
ABC
A
BC
be a triangle with
A
B
=
A
C
AB = AC
A
B
=
A
C
. Let
M
M
M
be the midpoint of
B
C
BC
BC
. Let the circles with diameters
A
C
AC
A
C
and
B
M
BM
BM
intersect at points
M
M
M
and
P
P
P
. Let
M
P
MP
MP
intersect
A
B
AB
A
B
at
Q
Q
Q
. Let
R
R
R
be a point on
A
P
AP
A
P
such that
Q
R
∥
B
P
QR \parallel BP
QR
∥
BP
. Prove that
C
P
CP
CP
bisects
∠
R
C
B
\angle RCB
∠
RCB
.
geometry