UPSC 2014 CDS II Math Paper

Draw DG || BF
In ΔADG,E is the midpoint of AD and EF || DG
∴ F is the mid-point of AG. (Converse of mid-point theorem)
⇒ AF = FG …..(1)
In Δ BFC, D is the mid-point of BC and DG||BF.∴ G is the mid-point of FC. (Converse of mid-point theorem)
⇒ FG = GC......(2)
From (a) and (b), we have
AF = FG = GC
∴AF=

AC

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