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Let AD be a median of the Delta ABC. If...

Let AD be a median of the `Delta ABC`.
If AE and AF are medians of the triangle ABD and ADC, respectively, and
`BD=a/2 AD = m_(1), AE = m_(2), AF = m_(3), " then a^(2)/8` is equal to

Text Solution

Verified by Experts

The correct Answer is:
`m_(2)^(2)+ m_(3)^(2) -2m_(1)^(2)`
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ARIHANT MATHS-PROPERTIES AND SOLUTION OF TRIANGLES -Exercise (Subjective Type Questions)
  1. In an obtuse angled triangle, the obtuse angle is (3pi)/4 and the othe...

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  2. If in trianlge ABC, a,b,c and angle A are given and c sin A lt a lt c,...

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  3. If P is a point on the altitude AD of the triangle ABC such the /C B P...

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  4. If R denotes circumradius, then in DeltaABC,(b^2-c^2)/(2aR) is equal t...

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  5. In DeltaABC, A = (2pi)/(3), b -c = 3 sqrt3 cm and " area of " Delta AB...

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  6. If Delta = a^(2)-(b-c)^(2), Delta is the area of the Delta ABC then ta...

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  7. In a DeltaABC, B=90^(@), AC=h and the length of perpendicular from B t...

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  8. If in a Delta ABC, sin ^(3) A + sin ^(3) B+ sin ^(3) C =3 sin A .Sin...

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  9. In a triangle ABC, if the sides a,b,c, are roots of x^3-11 x^2+38 x-40...

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  10. If the sides a,b,c are in A.P., prove that (tan)A/2+ (tan) c/2=2/3( co...

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  11. The sides of a triangle are in A.P. and its area is (3)/(5) th of an e...

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  12. If AD, BE and CF are the medians of a Delta ABC, then evaluate (AD^(2)...

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  13. Let AD be a median of the Delta ABC. If AE and AF are medians of the ...

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  14. Find the radian measure corresponding to following degree measure 3...

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  15. DeltaABC is equilateral triangle of side a. P lies on AB such that A i...

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  16. The base of a triangle is divided into three equal parts. If theta(1)...

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  17. Find the value of sin ((31pi)/3)

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  18. If the angle at the vertex of an isosceles triangle having the maximum...

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  19. Find the value of trigonometric function sin((5pi)/3)

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  20. Solve cos^2(4x) - cos^2(2x)

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