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From a point `O` in the interior of a ` A B C` , perpendiculars `O D ,\ O E` and `O F` are drawn to the sides `B C ,\ C A` and `A B` respectively. Prove that: (i) `A F^2+B D^2+C E^2=O A^2+O B^2+O C^2-O D^2-O E^2-O F^2` (ii) `A F^2+B D^2+C E^2=A E^2+C D^2+B F^2`

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NAGEEN PRAKASHAN ENGLISH-TRIANGLES -Exercise 6d
  1. triangleABC is an isosceles triangle with AC = BC. If AB^(2)= 2AC^(2) ...

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  2. In an equilateral triangleABC, AD is the altitude drawn from A on the ...

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  3. M and N are point on sides QR and PQ respectively of /\ PQR, right-an...

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  4. The given figure shows a triangle ABC, in which AB gt AC. E is the mi...

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  5. In a square ABCD, show that AC^(2) = 2AB^(2).

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  6. In a rhombus ABCD, prove that AC^(2) + BD^(2) = 4AB^(2)

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  7. In triangle ABC, angle A =90^(@), CA=AB and D is a point on AB produce...

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  8. In acute angled triangle ABC, AD is median and AE is altitude , prove...

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  9. The following figure shows a triangle ABC in which AD is a median and ...

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  10. From a point O in the interior of a A B C , perpendiculars O...

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  11. In an acute angled triangle ABC, AD is the median in it. then : AD^...

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  12. In a right triangle ABC, right angled at A, AD is drawn perpendicular ...

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  13. In the given figure , ABC is a right triangle, right angled at B. Medi...

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  14. In the given figure , angleQPR= 90^(@) QR = 26 cm PM = 6cm, MR = 8c...

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  15. Given a right angled triangleABC. The lengths of the sides containing ...

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  16. In an acute-angled triangle, express a median in terms of its sides...

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  17. In a quadrilateral ABCD, angleB=90^(@) and AD^(2)= AB^(2) + BC^(2)+CD^...

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  18. A B C is a right triangle right-angled at Ca n dA C=sqrt(3)B C . Prove...

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  19. In triangleABC , angleA= 60^(@) prove that BC^(2)= AB^(2)+AC^(2)- AB ....

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  20. In the adjoining figure, find x,y and h.

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