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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