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If alpha,beta,gamma, are lengths of the ...

If `alpha,beta,gamma`, are lengths of the altitudes of a triangle ABC with area `Delta `, then `Delta^2/R^2(1/alpha^2+1/beta^2+1/gamma^2)=`

A

`sin^(2)A+sinB+sin^(2)C`

B

`cos^(2)A+cos^(2)B+cos^(2)C`

C

`tan^(2)A+tan^(2)B+tan^(2)C`

D

`cot^(2)A+ cot^(2)B+cot^(2)C`

Text Solution

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The correct Answer is:
A
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AAKASH SERIES-PROPERTIES OF TRIANGLES-PRACTICE SHEET (EXERCISE-III) (LEVEL-I) (Straight Objective Type Questions)
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  2. If 2R+r=r(1) then

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  3. If r(1)=8, r(2)= 12r(3)=24 then C=

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  7. If a = 18 , b=24 , c=30 , find r(1) .

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  8. In DeltaABC, if C=90^(@) then R+r=

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  9. In DeltaABC,sqrt(rr1r2r3)/(2Rr(sinA+sinB+sinC)) =

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  10. (r+r(1))"tan"(B-C)/(2)+(r+r(2))"tan"(C-A)/(2)+(r+r(3))"tan"(A-B)/(2)=

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  11. In DeltaABC" prove that "cos^(2).(A)/(2)+cos^(2).(B)/(2)+cos^(2).(C)/...

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  12. In Delta ABC, the correct formule among the following are Statemen...

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  13. Which of the following statement is true : Statement -I : In Delt...

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  14. The radius of the circle passing through the centre of incircle of Del...

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  15. In a triangle ABC, tanA=2, tanB=(3)/(2) and side c= sqrt(65) then circ...

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  16. In a Delta ABC if angle A=90^@, then cos^(-1)(( R)/(r2 +r3)) is equal

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  17. If alpha,beta,gamma, are lengths of the altitudes of a triangle ABC wi...

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  18. If P(1),P(2),P(3) are the altitudes of the DeltaABC then , show that ...

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  19. The sides of a cyclic quadrilateral are 3,3,4,4 when its area is great...

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  20. r^(2) cot ""(A)/(2) cot ""(B)/(2) cot ""(C)/(2)

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