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Mathematics
Problem
If four points
P
,
Q
,
R
,
S
P, Q, R, S
P
,
Q
,
R
,
S
in the plane be taken and the square of the length of the tangents from
P
P
P
to the circle on
Q
R
QR
QR
as diameter be denoted by
{
P
,
Q
R
}
\{P, QR\}
{
P
,
QR
}
, show that
{
P
,
R
S
}
−
{
P
,
Q
S
}
+
{
Q
,
P
R
}
−
{
Q
,
R
S
}
=
0
\{P, RS\} - \{P, QS\} + \{Q, PR\} - \{Q, RS\} = 0
{
P
,
R
S
}
−
{
P
,
QS
}
+
{
Q
,
P
R
}
−
{
Q
,
R
S
}
=
0
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