in angle ABCD,AD is the median through A and D is the mid point of AD. BE is produced to meet AC in F. prove that AF=1/3 AC.
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Given BD=DC=21BC
AE=ED=21AD
BX is parallel to BF.
Consider traiangle BFC and DKC
∠BFC=∠DkC, ∠FCD=∠KCD
BFC and DKC are similar .(AAA similarity)
& KCFC=DCBC=21BCBC=2
⇒KCFC=2 ⇒KC=21FC
K is mid point of FC FK=KC ....(1)
Consider triangles AEF and AKD
∠EAF=∠DAK ∠BFA=∠DKA (size BF∣∣DK)
∴ΔAFE & ΔAKD are similar (AAA similirity )
⇒AKAF=ADAE=
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