MathDB
Problems
Contests
National and Regional Contests
Latvia Contests
Latvia BW TST
2020 Latvia Baltic Way TST
9
9
Part of
2020 Latvia Baltic Way TST
Problems
(1)
Existence of circle
Source: Latvian TST for Baltic Way 2020 P9
10/18/2020
Given
△
A
B
C
\triangle ABC
△
A
BC
, whose all sides have different length. Point
P
P
P
is chosen on altitude
A
D
AD
A
D
. Lines
B
P
BP
BP
and
C
P
CP
CP
intersect lines
A
C
,
A
B
AC, AB
A
C
,
A
B
respectively and point
X
,
Y
X, Y
X
,
Y
.It is given that
A
X
=
A
Y
AX=AY
A
X
=
A
Y
. Prove that there is circle, whose centre lies on
B
C
BC
BC
and is tangent to sides
A
C
AC
A
C
and
A
B
AB
A
B
at points
X
,
Y
X,Y
X
,
Y
.
geometry