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2023 UMD Math Competition Part I
#23
Assume a triangle
Assume a triangle
Source: UMD 2023 I #23
October 20, 2023
geometry
UMD
Problem Statement
Assume a triangle
A
B
C
ABC
A
BC
satisfies
∣
A
B
∣
=
1
,
∣
A
C
∣
=
2
|AB| = 1, |AC| = 2
∣
A
B
∣
=
1
,
∣
A
C
∣
=
2
and
∠
A
B
C
=
∠
A
C
B
+
9
0
∘
.
\angle ABC = \angle ACB + 90^\circ.
∠
A
BC
=
∠
A
CB
+
9
0
∘
.
What is the area of
A
B
C
?
ABC?
A
BC
?
a
.
6
/
7
b
.
5
/
7
c
.
1
/
2
d
.
4
/
5
e
.
3
/
5
\mathrm a. ~ 6/7\qquad \mathrm b.~5/7\qquad \mathrm c. ~1/2 \qquad \mathrm d. ~4/5 \qquad \mathrm e. ~3/5
a
.
6/7
b
.
5/7
c
.
1/2
d
.
4/5
e
.
3/5
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