In △TXM, we have
XM||BN {∵XM||AB}
∴
TBTX=TNTM
........(i)
In △TMC, we have
XN||CM {∵XN||AC}
∴
TXTC=TNTM .........(ii)
From equation (i) and (ii), we get
TBTX=TXTC
⇒ TX2=TB×TC (hence proved)