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show that r(2)r(3) +r(3) r(1)+ r (1) r(2...

show that `r_(2)r_(3) +r_(3) r_(1)+ r _(1) r_(2)=s^(2)`

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ARIHANT MATHS-PROPERTIES AND SOLUTION OF TRIANGLES -Exercise For Sesssion 3
  1. In any Delta ABC, show that cos A+ cos B+ cos C = (1+ (r )/(R )).

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  2. Prove that (r(1) -r)/(a) + (r(2) -r)/(b) = (c)/(r(3))

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  3. show that r(2)r(3) +r(3) r(1)+ r (1) r(2)=s^(2)

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  4. Show that (r(1)+ r (2))(r (2)+ r (3)) (r(3)+r(1))=4Rs^(2)

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  5. If r(1) +r(2)+ r = r(3), then show that Delta is right angled.

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  6. In an equilateral triangle, the in-radius, circum-radius and one of th...

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  7. Show that ((1)/(r (1))+ (1)/(r(2)))((1)/(r(2))+(1)/(r (1)))((1)/(r (3)...

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  8. The exradii r(1), r(2), r(3)" of "DeltaABC and in HP, show that a,b an...

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  9. In a DeltaABC, show that r(1)* r(2)* r(3)*r=Delta^(2).

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  10. If the angle opf a triangle are in the ratio 1:2:3, then show that the...

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  11. Show that, 4 R r cos ""A/2cos ""B/2 cos ""C/2 =Delta

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

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  13. In a triangle ABC,if 1/r1^2+1/r2^2+1/r3^2+1/r^2=

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  14. (r1-r)(r2-r)(r3-r)=4R r^2

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  15. Show that ((1)/(r (1))+ (1)/(r(2)))((1)/(r(2))+(1)/(r (3)))((1)/(r (3)...

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  16. Prove that (r+r1)tan((B-C)/2)+(r+r2)tan((C-A)/2)+(r+r3)tan((A-B)/2)=0

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  17. Show that (b-c)/(r (1))+ (c-a)/(r (2))+(c-a)/(r (3)) =0.

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  18. If the sides be a,b,c, than find (r(1)- r)(r (2)+r(3)).

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  19. If a,b,c are in AP, then show that r(1), r(2), r(3) are in HP.

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  20. In Delta ABC with usual notation r1/(bc)+r2/(ca)+r3/(ab) is

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