Given that ΔABC is the triangle whose sides are AB = c, AC = b, BC = a
And AD is the bisector of ∠A.
We know that altitude bisects the opposite side.
So, let BD = DC = x.
Since AD bisects ∠A,
AC/AB = CD/DB
Substituting the given values,
b/c = CD/(a-CD)
⇒ b( a – CD) = c (CD)
⇒ ba – b(CD) = c (CD)
⇒ ba = CD (b + c)
⇒ CD = ba/ (b + c)
Since CD = BD,
BD = ba/ (b + c)
BD = ba/(b + c) and DC = ba/(b + c)
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