Question

Given:

TC
,
PD
,
TP
tangent to circle
k(O) at C, D, and E respectively

TC
∥
PD
Prove:
TO
⊥
PO

Answer 1

`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`