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