Get Answers to all your Questions

header-bg qa

E is the mid-point of a median AD of \triangle ABC and BE is produced to meet AC at F. Show that AF=\frac{1}{3}AC .

Answers (1)

best_answer

Solution.
Given: In \triangle ABC, AD is a median and E is the mid-point of AD
To Prove: 
AF=\frac{1}{3}AC.
Construction: Draw DP\parallel EF and \triangle ABC as given

Proof: In
\triangle ADP, E is mid-point of AD and EF\parallel DB

So, F is mid-point of AP {converse of midpoint theorem}
In \triangle FBC, D is mid-point of BC and DP\parallel BF

So, P is mid-point of FC {converse of midpoint theorem}
Thus, AF = FP = PC
AF+FP+PC=AC=3AF
\therefore AF=\frac{1}{3}AC
Hence Proved

Posted by

infoexpert26

View full answer