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In A B C ,A D is the median through A a...

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`

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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
...
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RD SHARMA-QUADRILATERALS-All Questions
  1. In Figure, A D is the median and D E A Bdot Prove that B E is the med...

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  2. In a A B C , find the measures of the angles of the triangle formed b...

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  3. In A B C ,A D is the median through A and E is the mid-point of A D ....

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  4. In Figure, A D , and B E are medians of A B C and B E || D Fdot Prove...

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  5. P ,Q and R are, respectively, the mid-points of sides B C ,C A and A B...

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  6. P is the mid-point of side A B of a parallelogram A B C D . A Line thr...

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  7. In Figure, A B C D isa trapezium in which side A B is a parallel to si...

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  8. In Figure, A B C D is a parallelogram. E and F are the mid-points of t...

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  9. A B C D is a parallelogram. P is a point on A D such that A P=1/3A D a...

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  10. In a A B C ,\ B M\ a n d\ C N are perpendiculars from B\ a n d\ C r...

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  11. In triangle ABC, M ,N and P are the mid-points of A B ,A C and B C res...

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  12. Prove that the line segment joining the mid-points of the diagonals of...

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  13. In a triangle A B C median A D is produced to X such that A D=D Xdot P...

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  14. In Delta ABC the lines are drawn parallel to BC,CA and AB respectively...

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  15. A B C D is a kite having A B=A D and B C=C D . Prove that the figure f...

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  16. Prove that In a parallelogram, opposite side are equal

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  17. The opposite angles of a parallelogram are equal.

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  18. The sides B A and D C of a quadrilateral A B C D are produced as shown...

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  19. In a quadrilateral A B C D ,A O andB O are the bisectors of /A and /B ...

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  20. The angle of quadrilateral are respectively 100^@,98^@,92^@dot Find th...

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