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In an equilateral triangle show that the...

In an equilateral triangle show that the in-radius and the circum-radius are connected by `r =R/2.`

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

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  2. If the sides of a triangle are in the ratio 3 : 7 : 8, then find R : r

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  3. In an equilateral triangle show that the in-radius and the circum-radi...

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  4. In any DeltaABC, find sin A+sin B+ sin C.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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