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The perpendicular from A on side BC of a `DeltaABC` intersects BC at D such that `DB= 3CD` (see the given figure). Prove that `2AB^(2)= 2AC^(2)+BC^(2)`.

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The correct Answer is:
`2AB^(2)= 2AC^(2)+BC^(2)`
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KUMAR PRAKASHAN-TRIANGLES-EXERCISE 6.5
  1. Sides of triangles are given below, Determine which of them are right ...

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  2. PQR is a Deltaright angled at P and M is a point on QR such that PM bo...

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  3. In the given figure, ABD is a Deltaright angled at A and AC bot BD. Sh...

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  4. In the given figure, ABD is a triangle right angled at A and AC bot BD...

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  5. In the given figure, ABD is a triangle right angled at A and AC bot BD...

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  6. ABC is an isosceles triangle, right angled at C. Prove that AB^(2)= 2A...

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  7. ABC is an isosceles triangle, with AC= BC. If AB^(2)= 2AC^(2), prove ...

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

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

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  10. In the given figure, O is a point in the interior of a DeltaABC, OD bo...

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  11. In the given figure, O is a point in the interior of a DeltaABC, OD bo...

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

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

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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 dista...

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

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  17. The perpendicular from A on side BC of a DeltaABC intersects BC at D s...

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

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

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  20. Tick the correct answer and justify : In DeltaABC, AB= 6 sqrt(3), AC= ...

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