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If a,b,c are in HP, then prove that sin ...

If a,b,c are in HP, then prove that `sin ^(2) ""(A)/(2), sin ^(2) ""(B)/(2), sin ^(2) ""(C )/(2)` are also in HP.

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VMC MODULES ENGLISH-PROPERTIES OF TRIANGLE-Level - 2
  1. If cos theta=(a)/(b+c),cos phi=(b)/(a+c),cospsi=(c)/(a+b), where theat...

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  2. Given the base of a triangle, the opposite angle A, and the product k^...

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  3. If a,b,c are in HP, then prove that sin ^(2) ""(A)/(2), sin ^(2) ""(B)...

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  4. If in a triangle A B C ,cosA+2cosB+cosC=2 prove that the sides of the ...

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  5. Consider the following statements concerning a DeltaABC (i) The sid...

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  6. Prove that a triangle A B C is equilateral if and only if tanA+tanB+ta...

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  7. Let ABC be a triangle having O and I as its circumcentre and incentre,...

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  8. Let ABC be a triangle with incenter I and inradius r. Let D, E, and F ...

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  9. If In is the area of n-s i d e d regular polygon inscribed in a cir...

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  10. In a DeltaABC, if r(1) +r=r(2), then find the vlaue of (sec ^(2) A + c...

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  11. In DeltaABC, let b=6, c=10and r(1) =r(2)+r(3)+r then find area of Delt...

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  12. Consider on obtuse angle triangles with side 8 cm, 15 cm and xx cm (la...

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  13. letABC be a right angled triangle at C. If the inscribed circle touche...

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  14. Consider a Delta ABC and let a,b, and c denote the leghts of the sides...

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  15. In a DeltaABC, the internal bisector of angle ABC meets AC at k. if BC...

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  16. In DeltaABC has AC=13, AB=15 and BC=14. Let O be the circumcenter of t...

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  17. With usual notation in Delta ABC, the numerical value of ((a+b+c)/(r...

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  18. In a Delta ABC, cos A. cos C = (lambda(c^(2) - a^(2)))/(3 ca), if is t...

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  19. In a triangle ABC, medians AD and CE are drawn. If AD=5, angle DAC=pi/...

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  20. In a DeltaABC, the maximum value of 120((sum a cos ^(2)((A)/(2)))/(a+...

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