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In ΔABC, E is the mid -point of median AD such that BE produced meets AC at F. If AC = 10.5 cm,  then AF =



A

3 cm

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B

3.5 cm

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C

2.5 cm

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D

5 cm

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Solution

The correct option is A

3.5 cm


In ΔABC, E is the mid -point of median AD such that BE produced meets AC at F. Also, AC = 10.5 cm.

Draw DG || AF

In ΔADG

E is mid -point of AD and EF || DG

F is mid -point of AG

AF=FG                       ....(i)

In ΔBCF

D is mid -point of BC and DG || BF

G is mid -point of FC

FG=GC                         ....(ii)

From (i) and (ii)

AF = FG = GC = 13AC

But AC = 10.5 cm

AF=13AC=13×10.5=3.5cm

  


Mathematics
RD Sharma
Standard IX

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