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Question Number 114950 by joki last updated on 22/Sep/20

note the tringle ABC  is not isosceles with   the elevtions of AA1,BB1, and CC1.suppose  BA  amd CA respectively point at BB1 and  CC1 so that A1BA is pependiculer to BB1  and A1CA perpendiculer to CC1.the read   and BC lines intersect at the TA point.  define in the same way  TB and TC poits.  prove that TA,TB,and TC are collinear.

$${note}\:{the}\:{tringle}\:{ABC}\:\:{is}\:{not}\:{isosceles}\:{with}\: \\ $$$${the}\:{elevtions}\:{of}\:{AA}\mathrm{1},{BB}\mathrm{1},\:{and}\:{CC}\mathrm{1}.{suppose} \\ $$$${BA}\:\:{amd}\:{CA}\:{respectively}\:{point}\:{at}\:{BB}\mathrm{1}\:{and} \\ $$$${CC}\mathrm{1}\:{so}\:{that}\:{A}\mathrm{1}{BA}\:{is}\:{pependiculer}\:{to}\:{BB}\mathrm{1} \\ $$$${and}\:{A}\mathrm{1}{CA}\:{perpendiculer}\:{to}\:{CC}\mathrm{1}.{the}\:{read}\: \\ $$$${and}\:{BC}\:{lines}\:{intersect}\:{at}\:{the}\:{TA}\:{point}. \\ $$$${define}\:{in}\:{the}\:{same}\:{way}\:\:{TB}\:{and}\:{TC}\:{poits}. \\ $$$${prove}\:{that}\:{TA},{TB},{and}\:{TC}\:{are}\:{collinear}. \\ $$

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