or ▁passing ) ▁line ; ▁in ▁case ▁ ▁a ▁tang ent ▁line ▁and ▁if ▁ ▁the ▁line ▁is ▁a ▁sec ant ▁line . ▁( 2 ) ▁For ▁any ▁point ▁ ▁there ▁exists ▁exactly ▁one ▁tang ent ▁ ▁at ▁, ▁i . e ., ▁. ▁ ▁For ▁finite ▁plan es ▁( i . e . ▁the ▁set ▁of ▁points ▁is ▁finite ) ▁we ▁have ▁a ▁more ▁convenient ▁character ization : ▁ ▁For ▁a ▁finite ▁project ive ▁plane ▁of ▁order ▁ ▁( i . e . ▁any ▁line ▁contains ▁ ▁points ) ▁a ▁set ▁ ▁of ▁points ▁is ▁an ▁o val ▁if ▁and ▁only ▁if ▁ ▁and ▁no ▁three ▁points ▁are ▁col linear ▁( on ▁a ▁common ▁line ). ▁ ▁Pascal ' s ▁ 3 - point ▁version ▁▁ ▁Theorem ▁Let ▁be ▁ ▁an ▁o val ▁in ▁a ▁p app ian ▁project ive ▁plane ▁of ▁characteristic ▁. ▁▁ ▁is ▁a ▁non de generate ▁con ic ▁if ▁and ▁only ▁if ▁statement ▁( P 3 ) ▁holds : ▁▁ ▁( P 3 ): ▁ ▁Let ▁be ▁ ▁any ▁triangle ▁on ▁ ▁and ▁ ▁the ▁tang ent ▁at ▁point ▁ ▁to ▁, ▁then ▁the ▁points ▁▁▁ ▁are ▁col linear . ▁ ▁Proof ▁Let ▁the ▁project ive ▁plane ▁be ▁coordin at ized ▁in hom ogene ously ▁over ▁a ▁field ▁▁ ▁such ▁that ▁ ▁is ▁the ▁tang ent ▁at ▁, ▁the ▁x - axis ▁is ▁the ▁tang ent ▁at ▁the ▁point ▁▁ ▁and ▁▁ ▁contains ▁the ▁point ▁. ▁Furthermore , ▁we ▁set ▁ ▁( s . ▁image ) ▁The ▁o