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6
2020 Team #6
2020 Team #6
Source:
October 24, 2023
team test
geometry
Problem Statement
Triangle
△
A
B
C
\vartriangle ABC
△
A
BC
has side lengths
A
B
=
26
AB = 26
A
B
=
26
,
B
C
=
34
BC = 34
BC
=
34
, and
C
A
=
24
2
CA = 24\sqrt2
C
A
=
24
2
. A fourth point
D
D
D
makes a right angle
∠
B
D
C
\angle BDC
∠
B
D
C
. What is the smallest possible length of
A
D
‾
\overline{AD}
A
D
?
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