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Durer Math Competition
Durer Math Competition CD 1st Round - geometry
2022.C4
2022.C4
Part of
Durer Math Competition CD 1st Round - geometry
Problems
(1)
rectangle inscribed in triangle 2021-22 Dürer Round1 C4 D3
Source:
12/1/2022
We inscribed in triangle
A
B
C
ABC
A
BC
the rectangle
D
E
F
G
DEFG
D
EFG
such that
D
D
D
and
E
E
E
fall on side
A
B
AB
A
B
,
F
F
F
on side
B
C
BC
BC
, and
G
G
G
on side
A
C
AC
A
C
. We know that
A
F
AF
A
F
bisects angle
∠
B
A
C
\angle BAC
∠
B
A
C
, and that
A
D
D
E
=
1
2
\frac{AD}{DE} = \frac12
D
E
A
D
=
2
1
. What is the measure of angle
∠
C
A
B
\angle CAB
∠
C
A
B
?
geometry
rectangle
Durer