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The side B C of a triangle A B C is bise...

The side `B C` of a triangle `A B C` is bisected at `D ; O` is any point in `A D. BO and CO` produced meet `AC and AB` in `E and F` respectively and `A D` is produced to `X` so that `D` is the mid-point of `O X`. Prove that `A O : A X=A F : A B` and show that `FE||BC`.

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RD SHARMA ENGLISH-TRIANGLES-All Questions
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  2. Let A B C be a triangle and D and E be two points on side A B such tha...

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  3. The side B C of a triangle A B C is bisected at D ; O is any point in ...

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  7. O is any point inside a triangle A B C . The bisector of /A O B ,/B O ...

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  8. ABCD is a quadrilateral in which AB=AD . The bisector of  BAC a...

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  9. In /\A B C ,D is the mid-point of BC and ED is the bisector of the /A...

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  10. A D is a median of Delta A B C . The bisector of /A D B and /A D C...

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  11. In Figure, A B C is a right triangle right angled at B and points Da n...

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  12. In a triangle A B C , the angles at B and C are acute. If BE and CF b...

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  13. Prove that in any triangle the sum of squares of any two sides is equa...

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  14. AD is an altitude of an equilateral triangle ABC. On AD as base...

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  16. Prove that three times the sum of the squares of the sides of a tri...

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