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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+sin^2 B+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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A
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DIPTI PUBLICATION ( AP EAMET)-PROPERTIES OF TRIANGLES -EXERCISE 1A
  1. In Delta ABC, if (a+b+c)(a+b-c) =3ab, then C=

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  2. In Delta ABC if A=60^@, then the value of (1+a/c+b/c)(1+c/b-a/b)=

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  3. In Delta ABC, (cos A)/(c sin B)+(cos B)/( a sin C)+(cos C)/( b sin A)=

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  4. In Delta ABC , if ( sin A)/(4) = (sin B)/(5) = (sin C)/( 6) then th...

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  5. In Delta ABC, if a:b:c=3:4:5, then sin A:sin B:sin C=

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  6. In a /\ABC, if a:b:c = 7:8:9, then find cosA:cosB:cosC.

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  7. In Delta ABC if b+c:c+a:a+b=11:12:13, then cos A: cos B: cos C=

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  8. In Delta ABC, if cos A=17//22, cos C =1//14, then a:b:c=

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  9. In Delta ABC, if cot""A/2:cot""B/2:cot""C/2=3:7:9, then a:b:c=

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  10. In Delta ABC, if tanA: tan B: tan C=1:2:3, then sin A: sin B: sin C=

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  11. In a triangle ABC, (s-a)/11=(s-b)/12=(s-c)/13, then tan^2 (A//2)=

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  12. In a triangle ABC, if cot""A/2 cot""B/2=c, cot""B/2 cot""C/2=a and cot...

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  13. In Delta ABC, B=45^@, C=120^@,a=40 cm, the length of the perpendicular...

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  14. If H is the orthocentre of Delta ABC, then AH=

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  15. IF H is the orthocentre of Delta ABC and if AH=x, BH=y, CH=z, then a/x...

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  16. In Delta ABC, if (2 cos A)/a+ (cos B)/b+ (2 cos C)/c=a/(bc)+b/(ca), th...

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  17. If alpha,beta, gamma are the lengths of altitudes of Delta ABC, then a...

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

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  19. If alpha,beta,gamma are the lengths of the altitudes of Delta ABC, the...

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  20. IF alpha,beta,gamma are the lengths of the altitudes of Delta ABC, the...

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