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If P(1),P(2),P(3) are the altitudes of t...

If `P_(1),P_(2),P_(3)` are the altitudes of the `DeltaABC` then , show that `(1)/(P_(1)^(2))+(1)/(P_(2)^(2))+(1)/(P_(3)^(2))=(cotA+cotB+cotC)/(Delta)`

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The correct Answer is:
(1)&(2).L.H.S=R.H.S
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If p_1 , p_2 , p_3 are the altitudes drawn from the vertices A,B, C of triangles respectively show that (1)/( p_1) +(1)/(p_2) -(1)/( p_3) = ( 2ab cos ^(2) C//2) / ( Delta (a+b+ c) )

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SRISIRI PUBLICATION-PROPERTIES OF TRIANGLES-LAQ ,SAQ,VSAQ (2DHARDQ) (3DMIS.Q)
  1. In DeltaABC" show that "suma^(3)cos(B-C)=3abc

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  2. In DeltaABC" prove that "cos^(2).(A)/(2)+cos^(2).(B)/(2)+cos^(2).(C)/...

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  3. If P(1),P(2),P(3) are the altitudes of the DeltaABC then , show that ...

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  4. In DeltaABC" prove that "(b-c)^(2)cos^(2).(A)/(2)+(b+c)^(2)sin^(2).(A)...

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  5. Show that (c-bcosA)/(b-c"cos"A)=(cosB)/(cosC)

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  6. If b +c =3a , then find the value of cot.(B)/(2)cot.(C)/(2)

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  7. Show that 2("bc"cosA+"ca"cosB+"ab"cosC)=a^(2)+b^(2)+c^(2).

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  8. Prove that a(bcosC-c"cos"B)=b^(2)-c^(2)

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  9. If a=26,b-30,cosC=63//65 , then find c

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  10. If tan.(A)/(2)=(5)/(6)andtan.(C)/(2)=(2)/(5) then determine the relati...

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  11. Prove that (a^(2)+b^(2)-c^(2))/(c^(2)+a^(2)-b^(2))=(tanB)/(tanC)

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  12. What is the value of r/R in an equilateral triangle .

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  13. If rr(2)=r(1)r(3)then find B.

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  14. Express sumr(1)cot.(A)/(2) interms of s .

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  15. Show that rr(1)cot.(A)/(2)=Delta.

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  16. In DeltaABC , show that the sides a, b, c are in A.P ., if and only if...

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  17. If the lengths of the sides of a triangle are 3 , 4,5 find the circumr...

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  18. If the sides of a triangle are 13,14,15 , then find circum diameter .

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  19. If a=6 , b=5 ,c=9 then angle A .

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  20. If a =2 , b = 3 c=4 then find cos A .

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