In triangle ABC if b+c/11 = c+a/12 = a+b/13 PT cosA/7 = cosB/19 = cosC/25
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b+c/11 = c+a/12 = a+b/13=2(a+b+c)/36= (a+b+c)/18
Now b+c/11=(a+b+c)/18
⇒a/7=(a+b+c)/18
Similarly b/6= (a+b+c)/18
c/5=(a+b+c)/18
hence SinA/7=SinB/6=SinC
⇒
cosA/7 = cosB/19 = cosC/25
Now b+c/11=(a+b+c)/18
⇒a/7=(a+b+c)/18
Similarly b/6= (a+b+c)/18
c/5=(a+b+c)/18
hence SinA/7=SinB/6=SinC
⇒
cosA/7 = cosB/19 = cosC/25
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