If #1/(a+c)+1/(b+c)=3/(a+b+c)# then find angle C.?

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Answer 1 · 2018-01-16T16:17:27

Given

#1/(a+c)+1/(b+c)=3/(a+b+c)#

#=>(a+b+2c)(a+b+c)=3c^2+3ac+3bc+3ab#

#=>a^2+b^2+c^2+2ab+2bc+2ca+ca+bc+c^2=3c^2+3ca+3bc+3ab#

#=>a^2+b^2+2c^2 -3c^2=3ca-3ca+3bc-3bc+3ab-2ab#

#=>a^2+b^2-c^2=ab#

#=>(a^2+b^2-c^2)/(2ab)=(ab)/(2ab)#

#=>cosC=1/2=cos60^@#

#=>C=60^@#