Question

in a triangle ABC,AD is median F is the mid point on AC such that line BF bisect AD at E. If AD=14cm and AF=6cm. Find the measure of AC​

Answer 1

Step-by-step explanation:

Given

AD is the median of △ABC and E is the midpoint of AD

Through D

draw DG∥BF

In △ADG

E is the midpoint ofAD and EF∥DG

By converse of midpoint theorem we have

F is midpoint of AG and AF=FG ..............1

Similarly, in △BCF

D is the midpoint of BC and DG∥BF

G is midpoint of CF and FG=GC ..............2

From equations 1 and 2

we will get

AF=FG=GC ........3

AF+FG+GC=AC

AF+AF+AF=AC (from eu 3)

3AF=AC

AF= 1/3AC

Therefore, AF= 1/3 x 15 =5cm

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