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Show that r(r(1)+r(2)+r(3))=ab+bc+ca-s^(...

Show that `r(r_(1)+r_(2)+r_(3))=ab+bc+ca-s^(2).`

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The correct Answer is:
`ab+bc+ca-s^(2)=R.H.S`
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SRISIRI PUBLICATION-PROPERTIES OF TRIANGLES-LAQ
  1. Show that r(r(1)+r(2)+r(3))=ab+bc+ca-s^(2).

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  2. Prove that (r(1)(r(2)+r(3)))/(sqrt(r(1)r(2)+r(2)r(3)+r(3)r(1)))=a

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  3. Prove that 4(r(1)r(2)+r(2)r(3)+r(3)r(1))=(a+b+c)^(2)

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  4. Prove that ((1)/(r)-(1)/(r(1)))((1)/(r)-(1)/(r(2)))((1)/(r)-(1)/(r(3))...

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  5. Show that (r(1)+r(2))sec^(2).(C)/(2)=(r(2)+r(3))sec^(2).(A)/(2)=(r(3)+...

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  6. Show that r(1)+r(2)+r(3)-r=4R

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  7. Show that r+r(3)+r(1)-r(2)=4RcosB.

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  8. If A,A(1),A(2),A(3) are the areas of incircle and ex-circle of a trian...

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  9. In a DeltaABC" if " a =13,b=14,c=15 " then show that " R =(65)/(8),r=4...

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  10. In a DeltaABC " if " r(1)=8,r(2)=12,r(3)=24 find a, b,c .

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  11. If r(1)=2,r(2)=3,r(3)=6and r=1, prove that a=3,b=4 and c=5.

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  12. In DeltaABC" prove that " (r(1))/(bc)+(r(2))/(ca)+(r(3))/(ab)=(1)/(r)-...

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  13. In DeltaABC, " show that " (ab-r(1)r(2))/(r(3))=(bc-r(2)r(3))/(r(1))=(...

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  14. If p(1),p(2),p(3) are altitudes of a DeltaABC then show that (1)/(...

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

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

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  17. In DeltaABC , with usual notation show that ((a+b+c)^(2))/(a^(2)+b^(2)...

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  18. If a=(b+c)costheta, " then prove that" sintheta=(2sqrt(bc))/(b+c)cos((...

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  19. If a = (b-c) "sec" theta, then prove that tan theta = (2sqrt(bc))/(b-c...

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  20. In DeltaABC" prove that "acos^(2).(A)/(2)bcos^(2).(B)/(2)c"cos"^(2).(C...

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