MathDB
Problems
Contests
National and Regional Contests
Costa Rica Contests
Costa Rica - Final Round
2003 Costa Rica - Final Round
2
2
Part of
2003 Costa Rica - Final Round
Problems
(1)
Nice equality of segments
Source: Central American Olympiad 2003, Problem 2
5/23/2007
Let
A
B
AB
A
B
be a diameter of circle
ω
\omega
ω
.
ℓ
\ell
ℓ
is the tangent line to
ω
\omega
ω
at
B
B
B
. Take two points
C
C
C
,
D
D
D
on
ℓ
\ell
ℓ
such that
B
B
B
is between
C
C
C
and
D
D
D
.
E
E
E
,
F
F
F
are the intersections of
ω
\omega
ω
and
A
C
AC
A
C
,
A
D
AD
A
D
, respectively, and
G
G
G
,
H
H
H
are the intersections of
ω
\omega
ω
and
C
F
CF
CF
,
D
E
DE
D
E
, respectively. Prove that
A
H
=
A
G
AH=AG
A
H
=
A
G
.
geometry