Properties of Triangles 1 Question 18

18. If in a ABC,

2cosAa+cosBb+2cosCc=abc+bca

Then, the value of the A is degree.

(1993, 2M)

Analytical & Descriptive Questions

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Answer:

Correct Answer: 18. c=6,B=45 and A=75

Solution:

  1. Given, 2cosAa+cosBb+2cosCc=abc+bca

We know that, cosA=b2+c2a22bc

cosB=c2+a2b22ac and cosC=a2+b2c22ab

On putting these values in Eq. (i), we get

2(b2+c2a2)2abc+c2+a2b22abc+2(a2+b2c2)2abc=abc+bca2(b2+c2a2)+c2+a2b2+2(a2+b2c2)2abc=a2+b2abc3b2+c2+a2=2a2+2b2b2+c2=a2

Hence, the angle A is 90.



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