Question

AD is the medium of triangle ABC . E is the midpoint of AD . BE produced to meet AC at F . Show that AF = 1/3 AC

Answer 1

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Given AD is the median of ΔABC and E is the midpoint of An

 Through D, draw DG || BF In ΔADG, E is the midpoint of AD and EF ||

DG By converse of midpoint theorem we have F is midpoint of AG and

AF = FG  

→ (1) Similarly, in ΔBCF  D is the midpoint of BC and DG || BF    G is midpoint of CF and FG = GC → (2) From equations (1) and (2), we get AF

= FG = GC → (3) From the figure we have, AF + FG + GC = AC AF + AF + AF = AC [from (3)] 3 AF = AC AF = (1/3) AC

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Answer 2

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