SOLUTION: if in ABC triangle ∠C=60∘ then prove that 1/(a+c)+1/(b+c)=3/(a+b+c)
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Question 1005149: if in ABC triangle ∠C=60∘ then prove that 1/(a+c)+1/(b+c)=3/(a+b+c)
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Multiply both sides by (a+c)(b+c)(a+b+c) to clear out the fractions and make life easier. That is, statement holds if and only if
(a+b+c) + (a+c)(a+b+c) = 3(a+c)(b+c))
With some simplification, this is equivalent to
or
However this statement is true by applying the law of cosines on triangle ABC, as angle C = 60 degrees.
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