1.

In ` A B C ,A D`is the median through `A`and `E`is the mid-point of `A D`. `B E`produced meets `A C`in `F`(Figure). Prove that `A F=1/3A Cdot`

Answer» Construction
DK||BF
In`/_ADK` E is the midpoint od AD and EF||DK
F is the midpoint of AK
AF=FK-(1)
K is the mid point of FC
FK=KC-(2)
FK=KC=KC
AC=AF+FK+KC
AC=AF+AF+AF=3AF
`AF=1/3AC`.


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