Question

In the following figure, DE || AC and DC || AP. Prove that : `(BE)/(EC) = (BC)/(CP)`.

Answer 1

In the given figure,

DE || AC and DC || AP

To prove: `(BE)/(EC) = (BC)/(CP)`

Proof: In ΔBCA, we have

ED || CA

Since a line drawn is || to one side of a Δ divides the other two side proportionality.

∴ `(BE)/(EC) = (BD)/(DA)`   ...(i)

Similarly in ΔBPA; we have DC || AP

Since a line drawn is || to one side of a Δ divides the other two side proportionality.

∴ `(BC)/(CP) = (BD)/(DA)`   ...(ii)

From (i) and (ii),

`(BE)/(EC) = (BC)/(CP)`

Hence proved.