MathematicsChoose whether the given statement is true or false.Let X be any point on the side BC of a triangle ABC. If XM, XN are drawn parallel to BA and CA, BA in M, N respectively: MN meets BC produced in T then TX2=TB×TC. Is it true or False?

Choose whether the given statement is true or false.


Let X be any point on the side BC of a triangle ABC. If XM, XN are drawn parallel to BA and CA, BA in M, N respectively: MN meets BC produced in T then TX2=TB×TC. Is it true or False?


  1. A
    True
  2. B
    False 

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    Solution:

    It is being that XM is parallel to BA and XN is parallel to CA so, we can write it as: XM∥BA and  XN∥CA.
    https://www.vedantu.com/question-sets/24e89ad0-5194-44db-b73c-49470d3904bc7312702028344142831.png
    Consider  ΔTXM  here the line  XM∥BN  since line  XM∥BA, so by using the basic proportionality theorem we can write
    TBTX=TNTM--(i) 
    Now we consider the  ΔTMC, here by using the basic proportionality theorem we can write
    TXTC=TNTM--(ii) 
    Now from the equations (i) and (ii), we can write
    TBTX=TXTC 
    Hence by further solving the obtained equation we can say
    TX2 = TB⋅TC
    Hence proved that TX2=TB⋅TC. Hence Answer is True.
     
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