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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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To solve the problem, we need to analyze the given equation and find the angle \( B \) in triangle \( ABC \). ### Step-by-Step Solution: 1. **Start with the Given Equation**: \[ (a + b + c)(a - b + c) = 3ac \] ...
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CENGAGE ENGLISH-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 any DeltaABC , prove that (a-b)^(2)cos^(2)(C/2)+(a+b)^(2)sin^(2)(C ...

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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 = sqrt3, b = (1)/(2) (sqrt6 + sqrt2), and c = sqrt2, then find an...

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  5. The sides of a triangle are x^2+x+1, 2x+1 and x^2-1. Prove that the gr...

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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 , ba n dc be the three sides of a triangle, then prove that the ...

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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. For any triangle ABC, prove that a(bcosC-ccosB)=b^2-c^2

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

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

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  18. If cosA/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 the sides a , ba n dCof A B C are in AdotPdot, prove that 2sinA/2s...

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