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If p1 , p2 , p3 are the altitudes draw...

If ` p_1 , p_2 , p_3 ` are the altitudes drawn from the vertices A,B, C of triangles respectively show that
`(1)/( p_1) +(1)/(p_2) -(1)/( p_3) = ( 2ab cos ^(2) C//2) / ( Delta (a+b+ c) ) `

A

` (1)/( r_3) `

B

` r_1+r_2`

C

` r_3`

D

` ( 1)/ (r_1 ) `

Text Solution

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The correct Answer is:
A
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AAKASH SERIES-PROPERTIES OF TRIANGLES-EXERCISE - 1
  1. a cos ^(2) "" ( A) /(2) + b cos ^(2) "" ( B)/(2) = c cos ^(2) "" ( C...

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

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

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

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

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

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

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

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

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

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

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

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

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

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  15. In Delta ABC , " if " 2 r1 = 3r2= r3, then a: b: c =

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  16. In Delta ABC, if r1 lt r2 lt r3 then

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  17. In Delta ABC , " if" r1,r2,r3 are in H.P. then a,b,c are in

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  18. If A= 60 ^(@) " then " ( b) / ( c+ a) + ( c ) /( a+ b) =

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  19. If C= 60 ^(@) " then " ( a) /( b+ c) + ( b) /( c+a) =

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  20. (a ) /( b^(2) - c^(2)) + ( c )/( b^(2) - a^(2)) = 0 then B =

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