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Show that 16R^(2)r r(1) r (2) r(3)=a^(2)...

Show that `16R^(2)r r_(1) r _(2) r_(3)=a^(2) b ^(2) c ^(2)`

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Prove that r_(1)^(2)+r_(2)^(2) +r_(3)^(3) +r^(2) =16R^(2) -a^(2) -b^(2) -c^(2). where r= in radius, R = circumradius,, r_(1), r_(2), r_(3) are ex-radii.

In a triangleABC , if 1/r^(2) + 1/r_(1)^(2) + 1/r_(2)^(2) + 1/r_(3)^(2) = (a^(2) + b^(2) + c^(2))/(Delta^(n)) , then n is equal to ………..

If r_(1), r_(2) be the length of the perpendicular chords of the parabola y^(2) = 4ax drawn through the vertex, then show that (r_(1)r_(2))^(4//3) = 16a^(2)(r_(1)^(2//3) +r_(2)^(2//3))

" (i) Show that "r+r_(1)+r_(2)-r_(3)=4R cos C

Show that r_(1)+r_(2)=c cot((C)/(2))

Prove that r_(1) r_(2) + r_(2) r_(3) + r_(3) r_(1) = (1)/(4) (a + b + c)^(2)

Show that r_(1)+r_(2)=c cot ((C)/(2))

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ARIHANT MATHS-PROPERTIES AND SOLUTION OF TRIANGLES -Exercise For Sesssion 3
  1. If r(1) +r(2)+ r = r(3), then show that Delta is right angled.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  17. Show that r(1)+r(2)=c cot ((C)/(2))

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  18. Show that Rr (sin A+sin B + sin C) =Delta

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  19. Show that 16R^(2)r r(1) r (2) r(3)=a^(2) b ^(2) c ^(2)

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  20. If (r)/(r (1))= (r(2))/(r (3)), then show that c=90^(@).

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