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O is any point inside a rectangle. Prove...

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

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Let A B C D be a rectangle and P be any point in its plane. Show that A P^2+P C^2=P B^2+P D^2dot

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UNITED BOOK HOUSE-PATRASAYER BAMIRA GURUDAS INSTITUTION, BANKURA-EXERCISE
  1. If 1/x-1/y alpha 1/(y-x), show that x alpha y.

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  2. If ay - bx/c = cx - az/b = bz - cy/a, then prove that x/a = y/b = z/c.

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  3. If x/(y+z)=y/(z+x)=z/(x+y) prove that the value of each ratio is eithe...

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  4. State and prove Pythagoras theorem.

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  5. Prove that opposite angles of a cyclic quadrilateral are supplementary

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

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  7. ABCD is a cyclic quadrilaterla. Extended AB and DC intersect at P. Pr...

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  8. Geometrically calculate the value of sqrt(23). (Only traces of constru...

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  9. Draw a triangle whose one of the side is 7.2 cm and adjacent angles of...

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  10. Sum of two angles is 135^@ and their difference is pi^c/12. Find the s...

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  11. If costheta= x/sqrt(x^2+y^2) show that x sin theta = y cos theta.

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  12. If sin 17^@ = x/y show that sec 17^@-sin 73^@ = x^2/(ysqrt(y^2-x^2).

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  13. From a point on the roof of five storied building the angle of elevati...

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  14. Mohit, standing in the midst of a field, observes a flying birds in hi...

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  15. The curved surface of a solid metalic sphere is cut in such a way tha...

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  16. A right circular cylindrical tank of 9 metre height is filled with wat...

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  17. Half of the cuboidal water tank with length 2.1m and breadth of 1.5m i...

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  18. find the median of the following frequency distribution

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  19. Find the mode of the following frequency distribution.

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  20. Draw an ogiove (less than type) from the given data.

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