MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - College-Hosted Events
BMT Problems
2021 BMT
Tie 3
BMT 2021 Geometry Tiebreaker #3
BMT 2021 Geometry Tiebreaker #3
Source:
August 12, 2023
geometry
Problem Statement
Right triangle
△
A
B
C
\vartriangle ABC
△
A
BC
with its right angle at
B
B
B
has angle bisector
A
D
‾
\overline{AD}
A
D
with
D
D
D
on
B
C
‾
\overline{BC}
BC
, as well as altitude
B
E
‾
\overline{BE}
BE
with
E
E
E
on
A
C
‾
\overline{AC}
A
C
. If
D
E
‾
⊥
B
C
‾
\overline{DE} \perp \overline{BC}
D
E
⊥
BC
and
A
B
=
1
AB = 1
A
B
=
1
, compute
A
C
AC
A
C
.
Back to Problems
View on AoPS