Question

In ∆ ABC, AD is the median and E is the mid-point of AD. BE is produced meets AC at F. Given AC =9 cm then AF is
a) 4.5 cm b) 6 cm c) 3 cm d) 7.5 cm​

Answer 1

Given:

➨ AD is the median.

➨ E is the mid-point of AD.

➨ BE is produced meets AC at F.

➨ AC = 9 cm

To Find:

➟ AF = ?

Solution:

Draw DG || BF

In ∆BCF,

D is the mid-point of BC.

DG || BG

So, G is the mid-point of FC

⇰ GC = FG

In ∆ADG,

E is the mid-point of AD.

EF || DG

So, F is the mid-point of AG.

⇰ AF = FG

✰ AF = FG = GC

Now, we know that AC = AF + FG + GC

Thus,

AF = 1/3 AC

Value of AC is given = 9 cm ( substitute it's value )

AF = 1/3 × 9

AF = 3 cm

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