From a point outside a circle,
construct the tangent and secant line.Let the intersection point of the
tangent and the circle be T. Let the intersection points of the secant
and the circle be A and B. Then, PT PT =PAPB
If the points A and B lie on the half line with point P as an endpoint and point T does not lie on this half line, PT PT =PAPB, then the line PT is a tangent line of this circle passing through A, B, and T.
The common tangent line of two
PAPB = PCPD
Let the intersection point of extension lines of two chords AB and CD
in a circle be P. If PAPB = PCPD, then the four points A, B, C, and D lie
on a circle.
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