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In an equilateral triangle ABC, D is a point on BC such that `BD=1/3BC`. Prove that `9AD^(2)=7AB^(2)`.

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In an equilateral triangle ABC , D is a point on side BC such that BD = 1/3 BC . Prove that 9 AD^(2)=7AB^(2) .

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ZEN PUBLICATION-TRIANGLES-TEXTUAL EXERCISES (EXERCISE 2.5)
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  2. PQR is a triangle right angled at P and M is a point on QR such that P...

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  3. In the figure ABD is a triangle right-angled at A and AC|BD. Show that...

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  4. ABC is an isosceles triangle right-angled at C. Prove that AB^(2)=2AC^...

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

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

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  7. Prove that sum of the squares of the side of a rhombus is equal to th...

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

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  9. A ladder 10 m long reaches a window 8 m above the ground. Find the di...

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

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  11. An aeroplane leaves an airport and files due north at a speed of 1000...

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

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

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

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  15. In an equilateral triangle ABC, D is a point on BC such that BD=1/3BC....

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  16. In an equilateral triangle prove that three times the square of one si...

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  17. Tick the correct answer and justify : In DeltaABC,AB=6sqrt3cm, AC=12 c...

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