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If the diagonals of the quadrilateral ABCD intersect each other orthogonally,then prove that `AB^(2) + CD^(2) = BC^(2) + DA^(2)`

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CALCUTTA BOOK HOUSE-PYTHAGORAS THEOREM -LONG-ANSWER TYPE QUESTION
  1. ABC is an equilateral triangle. AD is perpendicular to BC. Prove that ...

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  2. ABC is a right-angled triangle of which /A = right angle. P and Q are...

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  3. If the diagonals of the quadrilateral ABCD intersect each other orthog...

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  4. AD is the height of the triangle ABC. If AB gt AC,then prove that AB^...

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  5. Two perpendicular BD and CE are drawn from the vertices B and C respe...

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  6. ABC is a right-angled isoscels triangles of which /C is a right angle...

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  7. In Delta ABC,/A = right angle. If CD is a median, then prove that BC^(...

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  8. OX,OY and OZ are the perpendiculars drawn from an internal point O of ...

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  9. In the Delta RST, /S right angle.X and Y are the midpoints of RS and ...

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  10. If in DeltaABC, AD| BC,then prove that AB^(2) + CD^(2) = AC^(2) + BD^...

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  11. Prove that the area of the square drawn on the diagonal of a square is...

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  12. O is any point inside a rectangle ABCD, Prove that OA^(2) + OC^(2)= OB...

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  13. ABCD is a rhombus.Prove that AB^(2) + BC^(2) +CD^(2) + DA^(2) = AC^(2)...

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  14. In Delta ABC, AD| BC . Prove thatAB^(2) - BD^(2) =AC^(2) -CD^(2)

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

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

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

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

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

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

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