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In fig., O is a point in the interior of a triangle ABC, OD ⊥ BC, OE ⊥ AC and OF ⊥ AB. Show that:- `O A^ 2 + O B^ 2 + O C^ 2 − O D^ 2 − O E^ 2 − O F^ 2 = A F^ 2 + B D^ 2 + C E^ 2`

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OSWAL PUBLICATION-TRIANGLES-NCERT CORNER ( TEXTBOOK QUESTIONS) ( EXERCISE - 6.5 )
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  2. PQR is a triangle right angled at P and M is a point on QR such that ...

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  3. In the figure given below ABC is a triangle right angled at A and AC b...

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  4. In the figure given below ABC is a triangle right angled at A and AC b...

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  5. In the figure given below ABC is a triangle right angled at A and AC b...

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  6. ABC is an isosceles triangle right angled at C. Prove that A B^2=2A C...

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  7. ABC is an isosceles triangle with AC = BC. If A B^2=2A C^2, prove tha...

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  8. ABC is an equilateral triangle of side 2a. Find each of its altitudes...

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  9. Prove that the sum of the squares of the sides of a rhombus is equa...

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  10. In fig., O is a point in the interior of a triangle ABC, OD ⊥ BC, OE...

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  11. In the figure given below O is a point in the interior of a triangle A...

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  12. A ladder 10m long reaches a window 8 m above the ground. Find the d...

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  13. A guy wire attached to a vertical pole of height 18m is 24m long an...

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  14. An aeroplane leaves an airport and flies due north at a speed of 1000...

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  15. Two poles of heights 6 m and 11m stand on a plane ground. If the di...

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  16. D and E are points on the sides CA and CB respectively of a triangle ...

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  17. The perpendicular from A on side BC of a ABC intersects BC at D such t...

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  18. In an equilateral triangle ABC, D is a point on side BC such that B D=...

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  19. In an equilateral triangle, prove that three times the square of on...

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  20. Tick the correct answer and justify : In DeltaPQR , PQ = 6sqrt(3) cm ...

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