MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - College-Hosted Events
UMD Math Competition
2023 UMD Math Competition Part I
#13
The orthocenter
The orthocenter
Source: UMD 2023 I #13
October 24, 2023
UMD
geometry
Problem Statement
The orthocenter of triangle
A
B
C
ABC
A
BC
lies on its circumcircle. One of the angles of
A
B
C
ABC
A
BC
must equal: (The orthocenter of a triangle is the point where all three altitudes intersect.)
a
.
3
0
∘
b
.
6
0
∘
c
.
9
0
∘
d
.
12
0
∘
e
.
It cannot be deduced from the given information.
\mathrm a. ~ 30^\circ\qquad \mathrm b.~60^\circ\qquad \mathrm c. ~90^\circ \qquad \mathrm d. ~120^\circ \qquad \mathrm e. ~\text{It cannot be deduced from the given information.}
a
.
3
0
∘
b
.
6
0
∘
c
.
9
0
∘
d
.
12
0
∘
e
.
It cannot be deduced from the given information.
Back to Problems
View on AoPS