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In Delta ABC, AD is a median and AM| BC....

In `Delta ABC`, AD is a median and AM`_|_` BC.Prove that
(a) `AC^(2) = AD^(2) +BC.DM+ ((BC)/(2))^(2)` (b) ` AB^(2) = AD^(2) -BC.DM+ ((BC)/(2))^(2)` (c ) `AC^(2) + AB^(2) = 2AD^(2) +(1)/(2) BC^(2)`

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CALCUTTA BOOK HOUSE-PYTHAGORAS THEOREM -LONG-ANSWER TYPE QUESTION
  1. In Delta ABC, AD| BC . Prove thatAB^(2) - BD^(2) =AC^(2) -CD^(2)

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  2. In Delta ABC , AD| BC which intersects BC at D. If BD =3 CD, then pro...

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  3. In the isosceles triangle ABC, AB=AC and BE is perpendicular to AC fro...

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  4. In an isosceles right-angled triangle ABC,/B=90^(@). The bisector of /...

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  5. Prove that the sum of the areas of the squares drawn on the sides of a...

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  6. Delta PQR is a right-angled isosceles triangle of which the two sides...

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  7. P is an external point of the square ABCD. If PA gt PB ,then prove tha...

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  8. In the right-angled ABC, /A =1 right angle. BE and CF are two medians...

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  9. A perpendicular AD is drawn on BC from the vertex A of the acute Delta...

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  10. Prove that if equilateral triangles are drawn on the sides of a right-...

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  11. O is an internal point of the rectangle PQRS. Prove that OQ^(2)+OS^(2)...

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  12. In the right-angled triangle ABC,/C = 90^(@).If the length of perpendi...

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  13. Delta ABC is an equilateral triangle . D is a point on the side BC su...

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  14. Prove that if the difference of the areas of the squares drawn on any...

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  15. In Delta ABC,AD is a perpendicular drawn from A to the side BC. If AD...

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  16. One of the two acute angles of a righ-angled triangle is twice the oth...

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  17. In Delta ABC, /A is a right angle and AO is perpendicular to BC. Prov...

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  18. Prove that in the quadrilateral of which the two diagonals intersect e...

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  19. Delta ABC is an obtus triangle in which /B = obtus angle. If AD is per...

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  20. In Delta ABC, AD is a median and AM| BC.Prove that (a) AC^(2) = AD^(...

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