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In Delta ABC Prove that sin ^(2) ""...

In ` Delta ABC ` Prove that
` sin ^(2) "" (A)/(2) + sin ^(2) ""(B) /(2) + sin ^(2) ""( C) /(2) =1 -( r) / ( 2R) `

A

` 2 + ( r )/( R ) `

B

` ( r )/( 2R ) `

C

` 1 + ( r ) /( 2 R) `

D

` 1- ( r ) /( 2 R) `

Text Solution

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The correct Answer is:
D
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AAKASH SERIES-PROPERTIES OF TRIANGLES-EXERCISE - 1
  1. If a = 13, b = 14 , c= 15 then r=

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  2. In Delta ABC Prove that cos A + cos B+ cos C =1 + ( r ) / ( R )

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  3. In Delta ABC Prove that sin ^(2) "" (A)/(2) + sin ^(2) ""(B) /(2...

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  4. ( a cos A + b cos B + c cos C )/( a +b +c ) =

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  5. ( a cot A + b cot B + c cot C )/( a + b+ c)

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  6. In Delta ABC , ( a )/( tan A) + ( b)/( tan B) + ( c )/( tan C) =

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  7. a cos ^(2) "" ( A) /(2) + b cos ^(2) "" ( B)/(2) = c cos ^(2) "" ( C...

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  8. In triangle ABC if p1, p2, p3 are the length of the altitudes from A, ...

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  9. If p1 , p2 , p3 are the altitudes drawn from the vertices A,B, C of ...

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  10. In Delta ABC if I is the incentre then the ratio IA : IB : IC is

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  11. If A1 , A2 , A3 are areas of excircles, A is the area of incircle of ...

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  12. If I is the incentre , A= 60 ^(@) then AI =

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  13. ( r1)/( (s.b) (s.c) )

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  14. In an equilateral triangle r:R:r1 is

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  15. In Delta ABC , if a= 30 , b= 24 , c= 18 , then the ratio ( 1)/(r1...

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  16. In Delta ABC , 4 ( r1r2 + r2r3+ r3r1) =

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  17. In Delta ABC, ( r3 + r1) sqrt([(r r2)/( r3r1) ]) =

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  18. In Delta ABC , ( r1-r)/( a) + ( r2-r)/( b) =

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  19. In Delta ABC , r ( r1 cot "" ( A) /(2) + r2 cot "" ( B) /( 2) + r3 ...

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  20. In Delta , " if " r1, r2, r3 are in H.P. then ( r2)/(r ) =

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