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In Delta ABC , if AD , BE , CF are the...

In ` Delta ABC , ` if AD , BE , CF are the perpendiculars drawn from the vertices A, B, C to the opposite sides, shot that
` (1)/( AD) + ( 1)/(BE) + (1)/(CF) = (1)/ ( r ) and (ii) AD . BE. CF = ((abc) ^(2))/( 8R^(3)) =( 8 Delta ^(3))/( abc) `

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SRISIRI PUBLICATION-PROPERTIES OF TRIANGLES-LAQ ,SAQ,VSAQ (2DHARDQ) (3DMIS.Q)
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  5. In DeltaABC" prove that "cos^(2).(A)/(2)+cos^(2).(B)/(2)+cos^(2).(C)/...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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