Q. 104.2( 13 Votes )

In the given figu

Answer :

We have the diagram as,


Given: BD = DC & OD = DX


To Prove: and also, EF BC


Proof: Since, from the diagram we can see that diagonals OX and BC bisect each other in quadrilateral BOCX. Thus, BOCX is a parallelogram.


If BOCX is a parallelogram, BX OC, and BO CX.


BX FC (as OC extends to FC) and CX BE (BO extends to BE)


BX OF and CX OE


BX OF, applying Thale’s theorem in ∆ABX, we get


…(i)


Now since CX OE, applying Thale’s theorem in ∆ACX, we get


…(ii)


By equations (i) and (ii), we get



By applying converse of Thale’s theorem in the above equation, we can write


EF BC


Hence, proved.


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