[tex]CO\: cuts\: PD\: at\: D_{1},TC\parallel PD\:(1)\\TC\: tangents\: to\: (O)\: at\: C\Rightarrow CO\perp TC\:at\:C\:(2)\\(1),(2)\Rightarrow CO\perp PD\: at\: D_{1}\: (3)\\PD\:tangents\: to\: (O)\: at\: D\Rightarrow OD\perp PD\: at\:D\:(4)\\(3),(4)\Rightarrow D\equiv D_{1}\Rightarrow C,O,D \:lie\: on\: a\: line\Rightarrow CD\:is\:the\:diameter\:of\:(O)\Rightarrow \widehat{CED}=90°\Rightarrow CE\perp DE\: at\: E\:(5)\\TC,TE\:are\:tangents\:to\:(O)\Rightarrow CE\perp TO\:(6)\\PD,PE\:are\:tangents\:to\:(O)\Rightarrow DE\perp PO\:(7)\\(5),(6),(7)\Rightarrow TO\perp PO[/tex]
