Question

In triangle ABC, AD is median through A and E is the mid point of AD. BE produced meets AC in F. Prove that AF = 1/3 AC.​

Answer 1

Answer:

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Step-by-step explanation:

To prove: AF = 1 3 13 AC

Construction: Through D, draw DK || BF

Proof: In ΔADK,

E is the mid-point of AD and EF || DK.

F is the mid-point of AK. (by converse of mid-point theorem)

⇒ AF = FK …(i)

In ΔBCF, D is the mid-point of BC and DK || BF. K is the mid-point of FC.

FK = KC …(ii)

From (i) and (ii),

we get AF = FK = KC …(iii)

Now, AC = AF + FK + KC

⇒ AC = AF + AF + AF [(using (iii)]

⇒ AC = 3AF

⇒ AF = 1 /2 AC