In triangle △ABC, the angle bisector AD from vertex A meets side BC at D. If BC = a, AC = b and AB = c, find CD in terms of a, b, c.

Introduction / Context:
The internal angle bisector theorem splits the opposite side in the ratio of adjacent sides. From that ratio and the total length of BC we can compute the exact lengths of BD and DC.

Given Data / Assumptions:

• AD is the internal bisector of ∠A, meeting BC at D.
• BC = a, AC = b, AB = c (standard notation).

Concept / Approach:

• Angle Bisector Theorem: BD/DC = AB/AC = c/b.
• Also BD + DC = a.
• Solve for DC from ratio and sum.

Step-by-Step Solution:

Verification / Alternative check:
Check the ratio: BD/DC = [a*c/(b+c)] / [a*b/(b+c)] = c/b, confirming the bisector property.

Why Other Options Are Wrong:

• Options with additions in numerators/denominators are algebraically inconsistent with BD/DC = c/b.
• None of these: Not applicable since CD = ab/(b + c) is exact.

Common Pitfalls:

• Inverting b and c (mixing up AB and AC).
• Forgetting BC = BD + DC = a.

Final Answer:
CD = (a b) / (b + c)