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

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

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Show that ((1)/(r _(1))+ (1)/(r_(2)))((1)/(r_(2))+(1)/(r _(3)))((1)/(r _(3))+(1)/(r_(1)))=(64 R^(3))/(a ^(2)b^(2) c^(2))

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

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

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

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

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

Show that (C_(0))/(1) - (C_(1))/(4) + (C_(2))/(7) - … + (-1)^(n) (C_(n))/(3n +1) = (3^(n) * n!)/(1*4*7…(3n+1)) , where C_(r) stands for ""^(n)C_(r) .

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

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

Statement I In a Delta ABC, if a lt b lt c and r is inradius and r_(1) , r_(2) , r_(3) are the exradii opposite to angle A,B,C respectively, then r lt r_(1) lt r_(2) lt r_(3). Statement II For, DeltaABC r_(1)r_(2)+r_(2)r_(3)+r_(3)r_(1)=(r_(1)r_(2)r_(3))/(r)

ARIHANT MATHS-PROPERTIES AND SOLUTION OF TRIANGLES -Exercise For Sesssion 3
  1. In an equilateral triangle, the inradius, circumradius, and one of the...

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

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  3. The ex-radii r(1), r(2), r(3) of a DeltaABC are in Hp, show that its s...

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

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  5. If l(1), l(2), l(3) are respectively the perpendicular from the vertic...

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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. If in Delta ABC, (a -b) (s-c) = (b -c) (s-a), prove that r(1), r(2), r...

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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. Prove that (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))+(a-b)/(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 in a triangle (r)/(r(1)) = (r(2))/(r(3)), then

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