MathDB
Problems
Contests
National and Regional Contests
China Contests
ASDAN Math Tournament
2019 ASDAN Math Tournament
7
7
Part of
2019 ASDAN Math Tournament
Problems
(1)
2019 Geometry # 7
Source:
9/10/2023
Consider a triangle
△
A
B
C
\vartriangle ABC
△
A
BC
with
A
B
=
7
AB = 7
A
B
=
7
,
B
C
=
8
BC = 8
BC
=
8
,
C
A
=
9
CA = 9
C
A
=
9
, and area
12
5
12\sqrt5
12
5
. We draw squares on each sides, namely
B
C
D
2
D
1
BCD_2D_1
BC
D
2
D
1
,
C
A
E
2
E
1
CAE_2E_1
C
A
E
2
E
1
and
A
B
F
2
F
1
ABF_2F_1
A
B
F
2
F
1
, so that the interiors of the squares do not intersect the interior of the triangle. What is the area of
△
D
2
E
2
F
2
\vartriangle D_2E_2F_2
△
D
2
E
2
F
2
?
geometry
2019