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In A B C ,= if (a+b+c)(a-b+c)=3a c , th...

In ` A B C ,=` if `(a+b+c)(a-b+c)=3a c ,` then find `/_Bdot`

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We have `(a + c)^(2) - b^(2) = 3ac`
or `a^(2) + c^(2) - b^(2) = ac`
But `cos B = (a^(2) + c^(2) -b^(2))/(2 ac) = (1)/(2)`
So, `B = (pi)/(3)`
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CENGAGE PUBLICATION-PROPERTIES AND SOLUTIONS OF TRIANGLE-Illustration
  1. The base of a triangle is divided into three equal parts. If t1, t2,t3...

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  2. In A B C , prove that (a-b)^2cos^2C/2+(a+b)^2sin^2C/2=c^2dot

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  3. In A B C ,= if (a+b+c)(a-b+c)=3a c , then find /Bdot

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  4. If a=sqrt(3),b=1/2(sqrt(6)+sqrt(2))dot and c=2, then find /A

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  5. The sides of a triangle are x^2+x+1,2x+1,a n dx^2-1 . Prove that the g...

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  6. If the angles A,B,C of a triangle are in A.P. and sides a,b,c, are in ...

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  7. Let a, b and c be the three sides of a triangle, then prove that the e...

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  8. Let alt=blt=c be the lengths of the sides of a triangle. If a^2+b^2<c^...

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  9. In a triangle ABC, if the sides a,b,c, are roots of x^3-11 x^2+38 x-40...

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  10. If in a triangle A B C ,/C=60^0, then prove that 1/(a+c)+1/(b+c)=3/(a+...

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  11. In a triangle, if the angles A , B ,a n dC are in A.P. show that 2cos1...

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  12. If a=9,b=4a n dc=8 then find the distance between the middle point of ...

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  13. Three parallel chords of a circle have lengths 2,3,4 units and subtend...

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  14. In a cyclic quadrilateral PQRS, PQ= 2 units, QR= 5 units, RS=3 units ...

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  15. Prove that a(bcosC-c cosB)=b^2-c^2

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  16. If in a triangle acos^2(C/2)+ c cos^2(A/2)=(3b)/2, then find the rela...

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  17. Prove that (b+c)cosA+(c+a)cosB+(a+b)cosC=2sdot

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  18. If cos(A/2)=sqrt((b+c)/(2c)) , then prove that a^2+b^2=c^2dot

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  19. If the cotangents of half the angles of a triangle are in A.P., then ...

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  20. If A, B and C are interior angles of a triangle ABC, then show that si...

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