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A perpendicular AD is drawn on BC from t...

A perpendicular AD is drawn on BC from the vertex A of the acute `Delta ABC`. Prove that `AC^(2) = AB^(2) +BC^(2) -2BC.BD`
OR
Prove that the square drawn on the opposite side of theacute angle of an acute triangle is equal to the areas of the sum of the squares drawn on its other two sides being subtracted by twice the area of the rectangle formed by one of its sides and the projection of the other side to this side.

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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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