Question

In triangle ABC, AD is the median from A and E is the mid-point of AD. BE produced meets AC in F and DGIIEF, meets AC in G. If AC- 5.4 cm. What is the length of AF?

Answer 1

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Answer 2

here is your answer OK

Given: AD is the median of ΔABC. E is the mid point of AD. BE produced meets AD at F

To Prove :

Construction: From Point D, draw DG BF.

Proof: In ΔADG, E is the mid-point of AD and EF||DG.

∴F is the mid point of AG [Converse of the mid point theorem]

⇒ AF = FG ... (i)

In ΔBCF, D is the mid point of BC and DG||BF

∴ G is the mid point of CF

⇒ FG = GC ... (ii)

From (i) and (ii), we get,

AF = FG = GC ... (iii)

Now, AF + FG + GC = AC

⇒ AF + AF + AF = AC [Using (iii)]

⇒ 3AF = AC

AF length 1.8
cm ok

hope help you