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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?

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True

False

answer is A.

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Detailed 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

\frac{TB}{TX} = \frac{TN}{TM} - - (i)

Now we consider the ΔTMC, here by using the basic proportionality theorem we can write

\Rightarrow \frac{TX}{TC} = \frac{TN}{TM} - - (ii)

Now from the equations (i) and (ii), we can write

\Rightarrow \frac{TB}{TX} = \frac{TX}{TC}

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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