MathDB
Problems
Contests
National and Regional Contests
Hungary Contests
Kürschák Math Competition
2004 Kurschak Competition
1
1
Part of
2004 Kurschak Competition
Problems
(1)
Mixtilinear circle
Source: Kürschák 2004, problem 1
7/13/2014
Given is a triangle
A
B
C
ABC
A
BC
, its circumcircle
ω
\omega
ω
, and a circle
k
k
k
that touches
ω
\omega
ω
from the outside, and also touches rays
A
B
AB
A
B
and
A
C
AC
A
C
in
P
P
P
and
Q
Q
Q
, respectively. Prove that the
A
A
A
-excenter of
△
A
B
C
\triangle ABC
△
A
BC
is the midpoint of
P
Q
‾
\overline{PQ}
PQ
.
geometry
circumcircle
geometry unsolved