I need to find out the x and y coordinates of the points where the common tangent touches the curve. How can I do this ?
Thanks a lot in advance.
Data points:
{{0,0},{1,-2.60788},{2,-4.42757},{3,-5.81138},{4,-6.90601},{5,-7.79825},{6,-8.52885},{7,-9.14314},{8,-9.64544},{9,-10.0547},{10,-10.3912},{11,-10.6627},{12,-10.8925},{13,-11.0713},{14,-11.2247},{15,-11.3377},{16,-11.424},{17,-11.4841},{18,-11.5183},{19,-11.5377},{20,-11.5467},{21,-11.5557},{22,-11.5551},{23,-11.5499},{24,-11.5393},{25,-11.5195},{26,-11.497},{27,-11.4729},{28,-11.4499},{29,-11.4331},{30,-11.4205},{31,-11.4144},{32,-11.4177},{33,-11.4222},{34,-11.4425},{35,-11.4702},{36,-11.492},{37,-11.5226},{38,-11.5466},{39,-11.5708},{40,-11.6143},{41,-11.6676},{42,-11.7275},{43,-11.8006},{44,-11.8758},{45,-11.9709},{46,-12.0729},{47,-12.1757},{48,-12.2869},{49,-12.401},{50,-12.5252},{51,-12.6564},{52,-12.7897},{53,-12.9267},{54,-13.0701},{55,-13.2254},{56,-13.3851},{57,-13.5441},{58,-13.711},{59,-13.8749},{60,-14.0373},{61,-14.2137},{62,-14.3937},{63,-14.576},{64,-14.754},{65,-14.9408},{66,-15.1289},{67,-15.3154},{68,-15.5015},{69,-15.6975},{70,-15.883},{71,-16.059},{72,-16.2309},{73,-16.4038},{74,-16.5645},{75,-16.7132},{76,-16.8584},{77,-16.9923},{78,-17.1227},{79,-17.2374},{80,-17.3432},{81,-17.438},{82,-17.5079},{83,-17.5681},{84,-17.615},{85,-17.6297},{86,-17.6146},{87,-17.5747},{88,-17.5074},{89,-17.4181},{90,-17.295},{91,-17.124},{92,-16.9207},{93,-16.6747},{94,-16.3812},{95,-16.0254},{96,-15.6106},{97,-15.1331},{98,-14.5669},{99,-13.918},{100,-13.1851},{101,-12.3401},{102,-11.3608},{103,-10.2353},{104,-8.91009},{105,-7.34354},{106,-5.4565},{107,-3.11396},{108,0}}
ListPlot[list]
gives,