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Geometry Mathley 2011-12
4.1
4.1
Part of
Geometry Mathley 2011-12
Problems
(1)
Geometry Mathley 4.1 P(1, 2)P(3, 4) = P(1, 4)P(2, 3) = P(1, 3)P(2, 4)
Source:
6/7/2020
Five points
K
i
,
i
=
1
,
2
,
3
,
4
K_i, i = 1, 2, 3, 4
K
i
,
i
=
1
,
2
,
3
,
4
and
P
P
P
are chosen arbitrarily on the same circle. Denote by
P
(
i
,
j
)
P(i, j)
P
(
i
,
j
)
the distance from
P
P
P
to the line passing through
K
i
K_i
K
i
and
K
j
K_j
K
j
. Prove that
P
(
1
,
2
)
P
(
3
,
4
)
=
P
(
1
,
4
)
P
(
2
,
3
)
=
P
(
1
,
3
)
P
(
2
,
4
)
P(1, 2)P(3, 4) = P(1, 4)P(2, 3) = P(1, 3)P(2, 4)
P
(
1
,
2
)
P
(
3
,
4
)
=
P
(
1
,
4
)
P
(
2
,
3
)
=
P
(
1
,
3
)
P
(
2
,
4
)
Bùi Quang Tuấn
distance
circle
geometry