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2021 MMATHS
10
10
Part of
2021 MMATHS
Problems
(1)
MMATHS 2021, Problem 10: Olympiad Geometry Medley
Source:
10/31/2021
Let
A
B
C
ABC
A
BC
be a triangle with circumcenter
O
O
O
and incenter
I
I
I
, and suppose that
O
I
OI
O
I
meets
A
B
AB
A
B
and
A
C
AC
A
C
at
P
P
P
and
Q
Q
Q
, respectively. There exists a point
R
R
R
on arc
B
A
C
^
\widehat{BAC}
B
A
C
such that the circumcircles of triangles
P
Q
R
PQR
PQR
and
A
B
C
ABC
A
BC
are tangent. Given that
A
B
=
14
AB = 14
A
B
=
14
,
B
C
=
20
BC = 20
BC
=
20
, and
C
A
=
26
CA = 26
C
A
=
26
, find
R
C
R
B
\frac{RC}{RB}
RB
RC
.Proposed by Andrew Wu
Yale
MMATHS