MathDB
Problems
Contests
National and Regional Contests
China Contests
ASDAN Math Tournament
2019 ASDAN Math Tournament
9
9
Part of
2019 ASDAN Math Tournament
Problems
(1)
2019 Geometry # 9
Source:
9/10/2023
Consider triangle
△
A
B
C
\vartriangle ABC
△
A
BC
with circumradius
R
=
10
R = 10
R
=
10
, inradius
r
=
2
r = 2
r
=
2
and semi-perimeter
S
=
18
S = 18
S
=
18
. Let
I
I
I
be the incenter, and we extend
A
I
AI
A
I
,
B
I
BI
B
I
and
C
I
CI
C
I
to intersect the circumcircle at
D
,
E
D, E
D
,
E
and
F
F
F
respectively. Compute the area of
△
D
E
F
\vartriangle DEF
△
D
EF
.
geometry
2019