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

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

O is any point inside a rectangle. Prove that OA^2+OC^2=OB^2+OD^2 .

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

ABC is a right triangle right angled at B. Let D and E be any points on AB and BC respectively. Prove that AE^(2) + CD^(2) = AC^(2) + DE^(2) .

‘O’ is any point in the interior of a triangle ABC. If OD bot BC, OE bot AC and OF bot AB, show that (i) OA^(2) + OB^(2) + OC^(2) - OD^(2) - OE^(2) - OF^(2) = AF^(2) + BD^(2) + CE^(2) (ii) AF^(2) + BD^(2) + CE^(2) = AE^(2) + CD^(2) + BE^(2) .

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

PQR is a triangle whose /_Q is right angle. If S is any point on QR, then prove that PS^(2) + QR^(2) =PR^(2) + QS^(2)

O is any point inside the rectangle ABCD. If OB = 6cm, OD = 8cm and OA = 5cm, then find the length of OC.

P is an external point of the square ABCD. If PA gt PB ,then prove that PA^(2) - PB^(2) ~= PD^(2) - PC^(2)

CALCUTTA BOOK HOUSE-PYTHAGORAS THEOREM -LONG-ANSWER TYPE QUESTION
  1. If in DeltaABC, AD| BC,then prove that AB^(2) + CD^(2) = AC^(2) + BD^...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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