MathDB
Problems
Contests
National and Regional Contests
Latvia Contests
Latvia BW TST
2015 Latvia Baltic Way TST
5
5
Part of
2015 Latvia Baltic Way TST
Problems
(1)
EF // AB wanted, line tangent to (ABC)
Source: 2015 Latvia BW TST P5
12/16/2022
B
E
BE
BE
is the altitude of acute triangle
A
B
C
ABC
A
BC
. The line
ℓ
\ell
ℓ
touches the circumscribed circle of the triangle
A
B
C
ABC
A
BC
at point
B
B
B
. A perpendicular
C
F
CF
CF
is drawn from
C
C
C
on line
ℓ
\ell
ℓ
. Prove that the lines
E
F
EF
EF
and
A
B
AB
A
B
are parallel.
geometry
parallel
circumcircle