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If p1,p2,p3 are the lengths of the altit...

If `p_1,p_2,p_3` are the lengths of the altitudes from the vertices A,B,C of ` Delta ABC ` to the opposite sides respectively then prove that
` p_1p_2p_3= ( (abc)^(2))/( 8R^(3)) = ( 8 Delta ^(3))/( abc) `

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AAKASH SERIES-PROPERTIES OF TRIANGLES-EXERCISE - 9.2 ( LONG ANSWER QUESTIONS)
  1. If r(1) = 2, r(2) = 3, r(3) = 6 and r =1, prove that a = 3, b=4 and c ...

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  2. If r1 = 36 , r2 = 18 and r3 = 12 then prove that a= 30 , b= 24 , c = ...

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  3. In a /\ABC if a = 13,b=14,c=15 then S.T R = (65)/8 , r=4, r(1) = (21)/...

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  4. If p1,p2,p3 are the lengths of the altitudes from the vertices A,B,C o...

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  5. If p1,p2,p3 are the lengths of the altitudes from the vertices A,B,C o...

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  6. If p1,p2,p3 are the lengths of the altitudes from the vertices A,B,C o...

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  7. If A,A(1),A(2),A(3) are the areas of incircle and ex-circle of a trian...

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  8. If (r2-r1) (r3-r1) =2r2r3. show that A = 90 ^(@) (1-(r1)/( r2))...

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  9. In Delta ABC, if (a-b) (s-c)= (b-c) (s-a) then r1,r2,r3 are in

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  10. Show that ( ab-r1r2)/(r3) = ( bc- r2r3)/( r1) = ( ca- r3r1)/( r2)

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  11. Prove that r1 +r2+r3-r = 4R

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  12. Prove that r+ r3 + r1 -r2= 4 R cos B

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  13. Prove that r+ r2 + r1 - r3 = 4 R cos C

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  14. If r1 + r2 = r 3 -r then show that | C = 90 ^(@)

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

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

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

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  18. In Delta ABC Prove that a cot A + b cot B + c cot C = 2 ( R + r)

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  19. In /\ABC prove that (r1)/(bc) + (r2)/(ca) + (r3)/(ab) = 1/r - 1/(2R).

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  20. In DeltaABC,r1r2sqrt[[(4R-r1-r2)/(r1+r2)])

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