MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - College-Hosted Events
CHMMC problems
2018 CHMMC (Fall)
10
10
Part of
2018 CHMMC (Fall)
Problems
(1)
2018 Fall Team #10
Source:
4/17/2022
Let
A
B
C
ABC
A
BC
be a triangle such that
A
B
=
13
AB = 13
A
B
=
13
,
B
C
=
14
BC = 14
BC
=
14
,
A
C
=
15
AC = 15
A
C
=
15
. Let
M
M
M
be the midpoint of
B
C
BC
BC
and define
P
≠
B
P \ne B
P
=
B
to be a point on the circumcircle of
A
B
C
ABC
A
BC
such that
B
P
⊥
P
M
BP \perp PM
BP
⊥
PM
. Furthermore, let
H
H
H
be the orthocenter of
A
B
M
ABM
A
BM
and define
Q
Q
Q
to be the intersection of
B
P
BP
BP
and
A
C
AC
A
C
. If
R
R
R
is a point on
H
Q
HQ
H
Q
such that
R
B
⊥
B
C
RB \perp BC
RB
⊥
BC
, find the length of
R
B
RB
RB
.
geometry