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

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

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Prove that (r_1-r)(r_2-r)(r_3-r)=4R r^2

If r_(1), r_(2) ,r_(3) are the ex-radii of DeltaABC, then prove that (bc)/(r_(1))+(ca)/(r _(2))+(ab)/(r _(3))=2R [((a)/(b)+(b)/a)+((b)/(c)+(c)/(b))+((c)/(a)+ (a)/(c))-3]

Let ABC be a triangle with incentre I and inradius r. Let D, E, F be the feet of the perpendiculars from I to the sides BC, CA and AB, respectively, If r_(2)" and "r_(3) are the radii of circles inscribed in the quadrilaterls AFIE, BDIF and CEID respectively, then prove that r_(1)/(r-r_(1))+r_(2)/(r-r_(2))+r_(3)/(r-r_(3))=(r_(1)r_(2)r_(3))/((r-r_(1))(r-r_(2))(r-r_(3)))

Prove that (r_(2) + r_(3))/(1 + cos A) = (r_(3) + r_(1))/(1 + cos B) = (r_(1) + r_(2))/(1+ cos C)

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Prove that (r_1+r_2)/(1+cosC)=2R

Prove that : (r_1)/(b c)+(r_2)/(c a)+(r_3)/(a b)=1/r-1/(2R)

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ARIHANT MATHS ENGLISH-PROPERTIES AND SOLUTION OF TRIANGLES -Exercise For Sesssion 3
  1. In any DeltaABC, find sin A+sin B+ sin C.

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  2. In any Delta ABC, show that cos A+ cos B+ cos C = (1+ (r )/(R )).

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

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

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

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

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  7. In an equilateral triangle, the inradius, circumradius, and one of the...

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

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  9. The exradii r(1), r(2), and r(3) " of " Delta ABC are in H.P. show tha...

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

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

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

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

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

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

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  16. Prove that (r1-r)(r2-r)(r3-r)=4R r^2

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

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

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

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