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If two circles touch each other (interna...

If two circles touch each other (internally or externally); the point of contact lies on the line through the centres.

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seg OT `_|_` line l …(Tangent theorem ) …(1)
seg PT `_|_` line l ….(Tangent theorem ) ….(2)
`:.` seg OT and seg PT are perpendiculars to line l at point T.
`:'` One and only one perpendicular can be drawn at a given point on a line.
`:.` Line OT and PT are not two different lines.
They are one and the same.
`:.` Point O,T and P are collinear.
`:.` Point T lies on line OP .
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