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2022 CHMMC Winter (2022-23)
5
CHMMC 2022 Winter / 2022-23 Team #5
CHMMC 2022 Winter / 2022-23 Team #5
Source:
August 10, 2023
geometry
Problem Statement
Let
A
B
C
ABC
A
BC
be a triangle with
A
B
=
6
AB = 6
A
B
=
6
,
A
C
=
8
AC = 8
A
C
=
8
,
B
C
=
7
BC = 7
BC
=
7
. Let
H
H
H
be the orthocenter of
A
B
C
ABC
A
BC
. Let
D
≠
H
D \ne H
D
=
H
be a point on
A
H
‾
\overline{AH}
A
H
such that
∠
H
B
D
=
3
2
∠
C
A
B
+
1
2
∠
A
B
C
−
1
2
∠
B
C
A
\angle HBD =\frac32 \angle CAB+ \frac12 \angle ABC - \frac12 \angle BCA
∠
H
B
D
=
2
3
∠
C
A
B
+
2
1
∠
A
BC
−
2
1
∠
BC
A
. Find
D
H
DH
DH
.
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