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Mathematics
Mathematics
Problem
Points
A
(
0
,
0
)
,
B
(
6
,
0
)
,
A(0,0),\; B(6,0),
A
(
0
,
0
)
,
B
(
6
,
0
)
,
and
C
(
2
,
4
)
C(2,4)
C
(
2
,
4
)
are fixed in the coordinate plane. Point
D
D
D
is chosen so that
∠
A
D
B
=
∠
A
C
B
\angle ADB = \angle ACB
∠
A
D
B
=
∠
A
C
B
. Prove that the points
A
,
B
,
C
,
A, B, C,
A
,
B
,
C
,
and
D
D
D
lie on a common circle.
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