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If R denotes the circum-radius of a Delt...

If R denotes the circum-radius of a `Delta ABC`, then `(b^(2)-c^(2))/(2aR)` is equal to

A

cos (B-C)

B

cos B-cosC

C

sin (B - C)

D

none of these

Text Solution

Verified by Experts

Using `a/(2sinA)=b/(2sinB)=c/(2sinC)=R` we get `(b^(2)-c^(2))/(2aR)=(4R^(2)(sin^(2)B-sin^(2)C))/(4R^(2)sinA)=(sin(B+C)sin(B-C))/(sinA)=sin(B-C)`
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OBJECTIVE RD SHARMA-PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM-Chapter Test
  1. If R denotes the circum-radius of a Delta ABC, then (b^(2)-c^(2))/(2aR...

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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. The area of the reactangle polygen of n sides is (where R is the radiu...

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  4. If the angles of a rectangle are 30^(@) and 45^(@) and the included si...

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  5. In a triagnle ABC, angle B=pi/3 " and " angle C = pi/4 let D divide ...

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  6. If A is the area and 2s the sum of the sides of a triangle,then

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  7. If in a triangle ABC, right angled at B, s-a=3, s-c=2, then the values...

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  8. If the sides of a triangle are a, b and sqrt(a^(2) + ab + b^(2)), then...

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  9. In a DeltaA B Csum(b+c)tanA/2tan((B-C)/2)=

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  10. In triangle ABC, angleA=pi/3 and b:c =2:3, tan theta=sqrt3/5, 0 lt the...

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  11. In a DeltaABC, AD is the altitude from A. Given bgtc ,angleC=23^(@) an...

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  12. If the angles A, B, C (in that order) of triangle ABC are in arithmeti...

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  13. If the radius of the incircle of a triangle withits sides 5k, 6k and 5...

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  14. Two sides of a triangle are 2sqrt2 and 2sqrt3cm and the angle opposite...

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  15. In a triangleABC, a=13cm, b=12 and c=5cm The distance of A from BC is

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  16. In a triangleABC,B=pi/8, C=(5pi)/(8). The altitude from A to the side ...

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  17. In a DeltaABC, A=(2pi)/3, b-c=3sqrt3 cm and area(DeltaABC)=(9sqrt3)/2 ...

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  18. In DeltaABC if a=(b-c)sectheta then (2sqrt(bc))/(b-c)sin(A/2)=

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  19. In a DeltaABC, (a + b + c) (b + c - a) = lambda bc. (where symbols ha...

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  20. If in DeltaABC, a=2b and A=3B, then A is equal to

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  21. Let the angles A , B and C of triangle A B C be in AdotPdot and let b ...

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