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CBSE Class 9 Answered

AD is a median of ∆ABC and E is the mid point of AD. BE produced meets AC in F. Prove that AF = 1/3 AC
Asked by dimplesharma0810 | 28 Feb, 2016, 08:56: AM
answered-by-expert Expert Answer
 
begin mathsize 14px style D r a w space D K parallel to B F. I n space triangle A D K comma space E space i s space t h e space m i d minus p o i n t space o f space A D space a n d space E F parallel to D K. rightwards double arrow F space i s space t h e space m i d minus p o i n t space o f space A K. rightwards double arrow A F equals F K space space space space space space.... left parenthesis 1 right parenthesis I n space triangle B C F comma space D space i s space t h e space m i d minus p o i n t space o f space B C space a n d space D K parallel to B F rightwards double arrow K space i s space t h e space m i d minus p o i n t space o f space F C rightwards double arrow F K equals K C space space space space space.... left parenthesis 2 right parenthesis F r o m space left parenthesis 1 right parenthesis space a n d space left parenthesis 2 right parenthesis comma space w e space h a v e A F plus F K plus K C space space space space space space space space.... left parenthesis 3 right parenthesis N o w comma space A C equals A F plus F K plus K C rightwards double arrow A C equals A F space plus A F plus A F rightwards double arrow A C equals 3 A F rightwards double arrow A F equals 1 third A C end style
Answered by Rashmi Khot | 29 Feb, 2016, 11:59: AM

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CBSE 9 - Maths
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