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Prove that bc cos^(2).(A)/(2) + ca cos^(...

Prove that `bc cos^(2).(A)/(2) + ca cos^(2).(B)/(2) + ab cos^(2).(C)/(2) = s^(2)`

A

`(s-a)^2`

B

`(s-b)^2`

C

`(s-c)^2`

D

`s^2`

Text Solution

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The correct Answer is:
D
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MOTION-SOLUTION OF TRIANGLE-EXERCISE -1
  1. In triangle ABC , prove that (b+c)cos A +(c+a)cos B +(a+b)cos C=a+b+c.

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  2. (b-c)/acos^2 (A/2)+(c-a)/bcos^2(B/2)+(a-b)/c cos^2(C/2)=

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  3. Prove that bc cos^(2).(A)/(2) + ca cos^(2).(B)/(2) + ab cos^(2).(C)/(2...

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  4. In a triangleABC, [tan(A/2) tan(C/2)] is equal to

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  5. In A B C , the median A D divides /B A C such that /B A D :/C A D=2:1...

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  6. If the median AD of triangle ABC makes an angle pi/4 with the side BC,...

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

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  8. If the area of triangleABC is triangle =a^(2) -(b-c)^(2), then: tanA =

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  9. If the sides of a triangles are 3:7:8, then ratio R:r

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  10. In a right angled triangle R is equal to

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  11. In a triangle a = 13 , b = 14, c = 15, r =

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  12. In an equilateral triangle, the inradius and the circumradius are conn...

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  13. In a triangle ABC, right angled at B, then

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  14. If the area of triangles is 100 sq. cm, r1= 10 cm and r2= 50 cm, then...

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  15. In a triangleABC, the inradius and three exradii are r,r1,r2" and "r3 ...

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  16. In a triangleABC if r1 lt r2 lt r3, then

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  17. In a triangle ABC, if (a-b)/(b-c)= (s-a)/(s-c), then r1,r2,r3 are in

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  18. If AD, BE and CF are the medians of a ABC ,then (AD^(2)+BE^(2)+CF^(2))...

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  19. In triangle ABC, line joining the circumcenter and orthocenter is para...

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  20. In a triangle ABC, angle A = 30^(2), BC = 2 + sqrt5, then find the dis...

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