MathDB
Problems
Contests
National and Regional Contests
Russia Contests
Sharygin Geometry Olympiad
2019 Sharygin Geometry Olympiad
16
16
Part of
2019 Sharygin Geometry Olympiad
Problems
(1)
Sharygin CR 2019 P16
Source: Sharygin CR 2019 P16 (Grade 9 - 11)
3/6/2019
Let
A
H
1
AH_1
A
H
1
and
B
H
2
BH_2
B
H
2
be the altitudes of triangle
A
B
C
ABC
A
BC
. Let the tangent to the circumcircle of
A
B
C
ABC
A
BC
at
A
A
A
meet
B
C
BC
BC
at point
S
1
S_1
S
1
, and the tangent at
B
B
B
meet
A
C
AC
A
C
at point
S
2
S_2
S
2
. Let
T
1
T_1
T
1
and
T
2
T_2
T
2
be the midpoints of
A
S
1
AS_1
A
S
1
and
B
S
2
BS_2
B
S
2
respectively. Prove that
T
1
T
2
T_1T_2
T
1
T
2
,
A
B
AB
A
B
and
H
1
H
2
H_1H_2
H
1
H
2
concur.
geometry