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Tuymaada Olympiad
2018 Tuymaada Olympiad
2
2
Part of
2018 Tuymaada Olympiad
Problems
(1)
Equal segments, circle tangent to sides of triangle
Source: Tuymaada 2018 Junior League/Problem 2
7/20/2018
A circle touches the side
A
B
AB
A
B
of the triangle
A
B
C
ABC
A
BC
at
A
A
A
, touches the side
B
C
BC
BC
at
P
P
P
and intersects the side
A
C
AC
A
C
at
Q
Q
Q
. The line symmetrical to
P
Q
PQ
PQ
with respect to
A
C
AC
A
C
meets the line
A
P
AP
A
P
at
X
X
X
. Prove that
P
C
=
C
X
PC=CX
PC
=
CX
.Proposed by S. Berlov
circles
tangent
geometry