Given: C∉ BD ,△ABC D∈ ray BC ,AB=AC=BC Prove: BD>DA>AB
1 answer:
Triangle ABC is equilateral, because AB=BC=AC=a. Then
m∠A=m∠B=m∠C=60°.
Let point D lie on the ray BC to the right from points B and C and let CD=x. Then BD=a+x, AB=a.
Consider triangle ACD. In this triangle, m∠ACD=180°-m∠ACB=180°-60°=120°.
By the cosine theorem,

Since
then

and

Therefore, you get double inequality
or 
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